This is pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6) (format=pdflatex 2007.5.18) 7 NOV 2008 18:28 entering extended mode %&-line parsing enabled. **monoid (./monoid.tex LaTeX2e <2005/12/01> Babel <v3.8h> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, arabic, basque, bulgarian, coptic, welsh, czech, slovak, german, ng erman, danish, esperanto, spanish, catalan, galician, estonian, farsi, finnish, french, greek, monogreek, ancientgreek, croatian, hungarian, interlingua, ibyc us, indonesian, icelandic, italian, latin, mongolian, dutch, norsk, polish, por tuguese, pinyin, romanian, russian, slovenian, uppersorbian, serbian, swedish, turkish, ukenglish, ukrainian, loaded. 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(/usr/local/texlive/2007/texmf-dist/tex/latex/amsfonts/umsb.fd File: umsb.fd 2002/01/19 v2.2g AMS font definitions ) LaTeX Font Info: Font shape `OT1/ptm/bx/n' in size <8> not available (Font) Font shape `OT1/ptm/b/n' tried instead on input line 2. LaTeX Font Info: Font shape `OT1/ptm/bx/n' in size <6> not available (Font) Font shape `OT1/ptm/b/n' tried instead on input line 2. LaTeX Font Info: Font shape `OT1/phv/m/n' will be (Font) scaled to size 9.85492pt on input line 3. [3 ] [4] [5]) \tf@toc=\write6 \openout6 = `monoid.toc'. [6] Chapter 1. LaTeX Font Info: Font shape `OT1/ptm/bx/n' in size <20.74> not available (Font) Font shape `OT1/ptm/b/n' tried instead on input line 94. LaTeX Font Info: Font shape `OMS/ptm/m/n' in size <10.95> not available (Font) Font shape `OMS/pzccm/m/n' tried instead on input line 120. Underfull \hbox (badness 7486) in paragraph at lines 120--121 []\OT1/pcr/m/n/10.95 AutomorphismGroup \OT1/ptm/m/n/10.95 ([][]7.4.1[][]) with ar-gu-ment sat-is-fy-ing \OT1/pcr/m/n/10.95 IsTransformationSemigroup [] Underfull \hbox (badness 10000) in paragraph at lines 125--126 []\OT1/pcr/m/n/10.95 IsomorphismSemigroups \OT1/ptm/m/n/10.95 ([][]7.7.5[][]) w ith both ar-gu-ments sat-is-fy-ing [] [7 ] Underfull \hbox (badness 3895) in paragraph at lines 127--128 \OT1/ptm/m/n/10.95 Installation of \OT1/phv/m/n/10.95 GRAPE \OT1/ptm/m/n/10.95 is de-scribed in the \OT1/pcr/m/n/10.95 README \OT1/ptm/m/n/10.95 file of the \ OT1/phv/m/n/10.95 GRAPE \OT1/ptm/m/n/10.95 dis-tri-bu-tion and [] Underfull \hbox (badness 4832) in paragraph at lines 127--128 \OT1/ptm/m/n/10.95 in the sec-tion en-ti-tled `In-stalling the GRAPE Pack-age' of the \OT1/phv/m/n/10.95 GRAPE \OT1/ptm/m/n/10.95 man-ual; see [][] [] Underfull \hbox (badness 10000) in paragraph at lines 129--130 []\OT1/ptm/m/n/10.95 If you want to take ad-van-tage of the on-line help fa-cil -i-ties in \OT1/phv/m/n/10.95 MONOID\OT1/ptm/m/n/10.95 , [] Underfull \hbox (badness 10000) in paragraph at lines 129--130 \OT1/ptm/m/n/10.95 then the \OT1/phv/m/n/10.95 gap-doc \OT1/ptm/m/n/10.95 pack- age Ver-sion 1.1 or higher is also re-quired; see [][] [] Underfull \hbox (badness 4193) in paragraph at lines 129--130 \OT1/pcr/m/n/10.95 http://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc/ [][] \ OT1/ptm/m/n/10.95 for fur-ther de-tails of how [] LaTeX Font Info: Font shape `OT1/phv/bx/n' in size <14.4> not available (Font) Font shape `OT1/phv/b/n' tried instead on input line 132. 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Underfull \hbox (badness 2846) in paragraph at lines 146--147 []\OT1/ptm/m/n/10.95 download the pack-age archive \OT1/pcr/m/n/10.95 monoid3r1 p3.tar.gz \OT1/ptm/m/n/10.95 or \OT1/pcr/m/n/10.95 monoid3r1p3.tar.bz2 \OT1/ptm /m/n/10.95 from [] [8] [9] Underfull \hbox (badness 3557) in paragraph at lines 227--228 []\OT1/ptm/m/n/10.95 the fol-low-ing new func-tions have been in-tro-duced: \OT 1/pcr/m/n/10.95 TransformationActionNC [] Underfull \hbox (badness 2626) in paragraph at lines 227--228 \OT1/ptm/m/n/10.95 ([][]2.1.6[][]), \OT1/pcr/m/n/10.95 SmallestIdempotentPower \OT1/ptm/m/n/10.95 ([][]2.2.6[][]), \OT1/pcr/m/n/10.95 IsKerImgOfTransformation \OT1/ptm/m/n/10.95 ([][]2.2.2[][]), [] Underfull \hbox (badness 10000) in paragraph at lines 227--228 \OT1/ptm/m/n/10.95 ([][]2.1.2[][]), \OT1/pcr/m/n/10.95 AsBooleanMatrix \OT1/ptm /m/n/10.95 ([][]2.3.1[][]), \OT1/pcr/m/n/10.95 KerImgOfTransformation \OT1/ptm/ m/n/10.95 ([][]2.2.3[][]), [] Underfull \hbox (badness 10000) in paragraph at lines 232--233 []\OT1/pcr/m/n/10.95 GradedImagesTransformationMonoid \OT1/ptm/m/n/10.95 was re -named [] Underfull \hbox (badness 10000) in paragraph at lines 234--235 []\OT1/pcr/m/n/10.95 GradedKernelsTransformationMonoid \OT1/ptm/m/n/10.95 was r e-named [] [10] [11] Chapter 2. 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lines 479--482 [] [14] Underfull \hbox (badness 10000) in paragraph at lines 505--508 [] Underfull \hbox (badness 10000) in paragraph at lines 535--538 [] Underfull \hbox (badness 10000) in paragraph at lines 554--557 [] [15] Underfull \hbox (badness 10000) in paragraph at lines 588--591 [] Underfull \hbox (badness 10000) in paragraph at lines 608--611 [] Underfull \hbox (badness 10000) in paragraph at lines 628--634 [] [16] Underfull \hbox (badness 10000) in paragraph at lines 667--670 [] Underfull \hbox (badness 10000) in paragraph at lines 701--704 [] [17] [18] Chapter 3. pdfTeX warning (ext4): destination with the same identifier (name{L.X7DFB63A97E 67C0A1}) has been already used, duplicate ignored <to be read again> \relax l.730 \hyperdef{L}{X7DFB63A97E67C0A1}{} Underfull \hbox (badness 10000) in paragraph at lines 751--754 [] Underfull \hbox (badness 10000) in paragraph at lines 769--772 [] [19 ] Underfull \hbox (badness 10000) in paragraph at lines 795--798 [] Underfull \hbox 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such that \OT1/pcr/m/n/10.95 OnSets(imgs[i], [] Underfull \hbox (badness 10000) in paragraph at lines 1213--1216 [] [26] [27] Chapter 4. pdfTeX warning (ext4): destination with the same identifier (name{L.X7DFB63A97E 67C0A1}) has been already used, duplicate ignored <to be read again> \relax l.1256 \hyperdef{L}{X7DFB63A97E67C0A1}{} [28 ] Underfull \hbox (badness 10000) in paragraph at lines 1325--1328 [] Underfull \hbox (badness 10000) in paragraph at lines 1344--1347 [] Underfull \hbox (badness 2126) in paragraph at lines 1349--1350 []\OT1/ptm/m/n/10.95 if \OT1/pcr/m/n/10.95 C \OT1/ptm/m/n/10.95 sat-is-fies \OT 1/pcr/m/n/10.95 IsGreensRClass \OT1/ptm/m/n/10.95 (\OT1/ptm/b/n/10.95 Reference : Is-Green-sR-Class\OT1/ptm/m/n/10.95 ), then \OT1/pcr/m/n/10.95 GreensRClassDa ta [] Underfull \hbox (badness 10000) in paragraph at lines 1349--1350 \OT1/ptm/m/n/10.95 re-turns an ob-ject in the cat-e-gory \OT1/pcr/m/n/10.95 IsG reensRClassData \OT1/ptm/m/n/10.95 ([][]4.2.6[][]) with rep-re-sen-ta-tion [] [29] Underfull \hbox (badness 10000) in paragraph at lines 1357--1358 \OT1/ptm/m/n/10.95 The com-po-nents \OT1/pcr/m/n/10.95 strongorb\OT1/ptm/m/n/10 .95 , \OT1/pcr/m/n/10.95 perms\OT1/ptm/m/n/10.95 , and \OT1/pcr/m/n/10.95 schut z \OT1/ptm/m/n/10.95 are ob-tained us-ing the func-tion [] Underfull \hbox (badness 10000) in paragraph at lines 1377--1380 [] Underfull \hbox (badness 2229) in paragraph at lines 1382--1383 []\OT1/ptm/m/n/10.95 if \OT1/pcr/m/n/10.95 C \OT1/ptm/m/n/10.95 sat-is-fies \OT 1/pcr/m/n/10.95 IsGreensLClass \OT1/ptm/m/n/10.95 (\OT1/ptm/b/n/10.95 Reference : Is-GreensLClass\OT1/ptm/m/n/10.95 ), then \OT1/pcr/m/n/10.95 GreensLClassData [] Underfull \hbox (badness 10000) in paragraph at lines 1382--1383 \OT1/ptm/m/n/10.95 re-turns an ob-ject in the cat-e-gory \OT1/pcr/m/n/10.95 IsG reensLClassData \OT1/ptm/m/n/10.95 ([][]4.2.6[][]) with rep-re-sen-ta-tion [] [30] Underfull \hbox (badness 10000) in paragraph at lines 1418--1421 [] Underfull \hbox (badness 2027) in paragraph at lines 1423--1424 []\OT1/ptm/m/n/10.95 if \OT1/pcr/m/n/10.95 C \OT1/ptm/m/n/10.95 sat-is-fies \OT 1/pcr/m/n/10.95 IsGreensHClass \OT1/ptm/m/n/10.95 (\OT1/ptm/b/n/10.95 Reference : Is-Green-sH-Class\OT1/ptm/m/n/10.95 ), then \OT1/pcr/m/n/10.95 GreensLClassDa ta [] Underfull \hbox (badness 10000) in paragraph at lines 1423--1424 \OT1/ptm/m/n/10.95 re-turns an ob-ject in the cat-e-gory \OT1/pcr/m/n/10.95 IsG reensHClassData \OT1/ptm/m/n/10.95 ([][]4.2.6[][]) with rep-re-sen-ta-tion [] Underfull \hbox (badness 10000) in paragraph at lines 1445--1448 [] Underfull \hbox (badness 2126) in paragraph at lines 1450--1451 []\OT1/ptm/m/n/10.95 if \OT1/pcr/m/n/10.95 C \OT1/ptm/m/n/10.95 sat-is-fies \OT 1/pcr/m/n/10.95 IsGreensDClass \OT1/ptm/m/n/10.95 (\OT1/ptm/b/n/10.95 Reference : Is-Greens-D-Class\OT1/ptm/m/n/10.95 ), then \OT1/pcr/m/n/10.95 GreensDClassDa ta [] Underfull \hbox (badness 10000) in paragraph at lines 1450--1451 \OT1/ptm/m/n/10.95 re-turns an ob-ject in the cat-e-gory \OT1/pcr/m/n/10.95 IsG reensDClassData \OT1/ptm/m/n/10.95 ([][]4.2.6[][]) with rep-re-sen-ta-tion [] [31] Underfull \hbox (badness 10000) in paragraph at lines 1476--1491 [] Underfull \hbox (badness 10000) in paragraph at lines 1493--1494 []\OT1/ptm/m/n/10.95 returns \OT1/pcr/m/n/10.95 true \OT1/ptm/m/n/10.95 if \OT1 /pcr/m/n/10.95 obj \OT1/ptm/m/n/10.95 lies in the cat-e-gory \OT1/pcr/m/n/10.95 IsGreensData\OT1/ptm/m/n/10.95 , \OT1/pcr/m/n/10.95 IsGreensRClassData\OT1/ptm /m/n/10.95 , [] Underfull \hbox (badness 1648) in paragraph at lines 1493--1494 \OT1/pcr/m/n/10.95 IsGreensLClassData\OT1/ptm/m/n/10.95 , \OT1/pcr/m/n/10.95 Is GreensHClassData\OT1/ptm/m/n/10.95 , \OT1/pcr/m/n/10.95 IsGreensDClassData\OT1/ ptm/m/n/10.95 , re-spec-tively. The ob- [] Underfull \hbox (badness 1917) in paragraph at lines 1493--1494 \OT1/ptm/m/n/10.95 and \OT1/pcr/m/n/10.95 DClassData \OT1/ptm/m/n/10.95 ([][]4. 2.7[][]) lie in the cat-e-gories \OT1/pcr/m/n/10.95 IsGreensRClassData\OT1/ptm/ m/n/10.95 , \OT1/pcr/m/n/10.95 IsGreensLClassData\OT1/ptm/m/n/10.95 , [] Underfull \hbox (badness 10000) in paragraph at lines 1499--1511 [] Underfull \hbox (badness 10000) in paragraph at lines 1513--1514 []\OT1/ptm/m/n/10.95 These func-tion con-struct ob-jects in the cat-e-gories \O T1/pcr/m/n/10.95 IsGreensRClassData \OT1/ptm/m/n/10.95 ([][]4.2.6[][]), [] Underfull \hbox (badness 2922) in paragraph at lines 1513--1514 \OT1/ptm/m/n/10.95 sub-cat-e-gories of \OT1/pcr/m/n/10.95 IsGreensData \OT1/ptm /m/n/10.95 ([][]4.2.6[][]) us-ing the out-put from \OT1/pcr/m/n/10.95 GreensRCl assData \OT1/ptm/m/n/10.95 ([][]4.2.2[][]), [] Underfull \hbox (badness 10000) in paragraph at lines 1519--1531 [] Underfull \hbox (badness 10000) in paragraph at lines 1533--1534 []\OT1/ptm/m/n/10.95 returns \OT1/pcr/m/n/10.95 true \OT1/ptm/m/n/10.95 if \OT1 /pcr/m/n/10.95 obj \OT1/ptm/m/n/10.95 has \OT1/pcr/m/n/10.95 IsGreensRClassData Rep\OT1/ptm/m/n/10.95 , \OT1/pcr/m/n/10.95 IsGreensLClassDataRep\OT1/ptm/m/n/10 .95 , [] [32] Underfull \hbox (badness 10000) in paragraph at lines 1542--1545 [] Underfull \hbox (badness 10000) in paragraph at lines 1578--1581 [] Underfull \hbox (badness 10000) in paragraph at lines 1583--1584 []\OT1/ptm/m/n/10.95 if \OT1/pcr/m/n/10.95 D \OT1/ptm/m/n/10.95 sat-is-fies \OT 1/pcr/m/n/10.95 IsGreensRClassData \OT1/ptm/m/n/10.95 ([][]4.2.6[][]), \OT1/pcr /m/n/10.95 IsGreensLClassData \OT1/ptm/m/n/10.95 ([][]4.2.6[][]), [] Underfull \hbox (badness 1655) in paragraph at lines 1583--1584 \OT1/pcr/m/n/10.95 IsGreensHClassData \OT1/ptm/m/n/10.95 ([][]4.2.6[][]), or \O T1/pcr/m/n/10.95 IsGreensDClassData \OT1/ptm/m/n/10.95 ([][]4.2.6[][]), then \O T1/pcr/m/n/10.95 SchutzenbergerGroup [] [33] Underfull \hbox (badness 10000) in paragraph at lines 1607--1610 [] Underfull \hbox (badness 10000) in paragraph at lines 1641--1644 [] [34] Chapter 5. pdfTeX warning (ext4): destination with the same identifier (name{L.X7DFB63A97E 67C0A1}) has been already used, duplicate ignored <to be read again> \relax l.1666 \hyperdef{L}{X7DFB63A97E67C0A1}{} [35 ] Underfull \hbox (badness 10000) in paragraph at lines 1726--1729 [] [36] Underfull \hbox (badness 10000) in paragraph at lines 1751--1757 [] Underfull \hbox (badness 10000) in paragraph at lines 1784--1787 [] Underfull \hbox (badness 10000) in paragraph at lines 1804--1807 [] [37] Underfull \hbox (badness 10000) in paragraph at lines 1828--1831 [] Underfull \hbox (badness 10000) in paragraph at lines 1848--1851 [] Underfull \hbox (badness 10000) in paragraph at lines 1871--1874 [] [38] Underfull \hbox (badness 10000) in paragraph at lines 1894--1897 [] Underfull \hbox (badness 10000) in paragraph at lines 1919--1922 [] Underfull \hbox (badness 10000) in paragraph at lines 1944--1947 [] [39] Underfull \hbox (badness 10000) in paragraph at lines 1967--1970 [] Underfull \hbox (badness 10000) in paragraph at lines 1991--1994 [] Underfull \hbox (badness 10000) in paragraph at lines 2018--2021 [] [40] Underfull \hbox (badness 10000) in paragraph at lines 2045--2048 [] Underfull \hbox (badness 10000) in paragraph at lines 2070--2073 [] Underfull \hbox (badness 10000) in paragraph at lines 2092--2095 [] [41] [42] Chapter 6. Underfull \hbox (badness 10000) in paragraph at lines 2126--2129 [] Underfull \hbox (badness 10000) in paragraph at lines 2153--2156 [] [43 ] ! LaTeX Error: There's no line here to end. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.2181 Your command was ignored. Type I <command> <return> to replace it with another command, or <return> to continue without it. Underfull \hbox (badness 10000) in paragraph at lines 2199--2202 [] Underfull \hbox (badness 10000) in paragraph at lines 2236--2239 [] [44] Underfull \hbox (badness 10000) in paragraph at lines 2266--2269 [] Underfull \hbox (badness 10000) in paragraph at lines 2287--2290 [] [45] Underfull \hbox (badness 10000) in paragraph at lines 2311--2314 [] Underfull \hbox (badness 10000) in paragraph at lines 2330--2333 [] Underfull \hbox (badness 10000) in paragraph at lines 2349--2352 [] Underfull \hbox (badness 10000) in paragraph at lines 2380--2383 [] [46] Underfull \hbox (badness 10000) in paragraph at lines 2397--2400 [] Underfull \hbox (badness 10000) in paragraph at lines 2414--2417 [] Underfull \hbox (badness 10000) in paragraph at lines 2435--2438 [] [47] Chapter 7. pdfTeX warning (ext4): destination with the same identifier (name{L.X7DFB63A97E 67C0A1}) has been already used, duplicate ignored <to be read again> \relax l.2460 \hyperdef{L}{X7DFB63A97E67C0A1}{} Underfull \hbox (badness 7486) in paragraph at lines 2490--2491 []\OT1/pcr/m/n/10.95 AutomorphismGroup \OT1/ptm/m/n/10.95 ([][]7.4.1[][]) with ar-gu-ment sat-is-fy-ing \OT1/pcr/m/n/10.95 IsTransformationSemigroup [] Underfull \hbox (badness 10000) in paragraph at lines 2495--2496 []\OT1/pcr/m/n/10.95 IsomorphismSemigroups \OT1/ptm/m/n/10.95 ([][]7.7.5[][]) w ith both ar-gu-ments sat-is-fy-ing [] [48 ] Underfull \hbox (badness 10000) in paragraph at lines 2502--2505 [] Underfull \hbox (badness 10000) in paragraph at lines 2521--2527 [] Overfull \hbox (20.22646pt too wide) in paragraph at lines 2529--2530 []\OT1/ptm/m/n/10.95 returns a semi-group ho-mo-mor-phism with rep-re-sen-ta-ti on \OT1/pcr/m/n/10.95 IsSemigroupHomomorphismByFunctionRep [] Underfull \hbox (badness 10000) in paragraph at lines 2557--2563 [] [49] Overfull \hbox (42.56435pt too wide) in paragraph at lines 2565--2566 []\OT1/ptm/m/n/10.95 returns a semi-group ho-mo-mor-phism with rep-re-sen-ta-ti on \OT1/pcr/m/n/10.95 IsSemigroupHomomorphismByImagesOfGensRep [] Underfull \hbox (badness 10000) in paragraph at lines 2591--2597 [] Overfull \hbox (9.05751pt too wide) in paragraph at lines 2599--2600 []\OT1/ptm/m/n/10.95 returns a semi-group ho-mo-mor-phism with rep-re-sen-ta-ti on \OT1/pcr/m/n/10.95 IsSemigroupHomomorphismByImagesRep [] [50] Underfull \hbox (badness 10000) in paragraph at lines 2636--2642 [] Underfull \hbox (badness 10000) in paragraph at lines 2669--2672 [] Underfull \hbox (badness 10000) in paragraph at lines 2689--2692 [] Underfull \hbox (badness 1418) in paragraph at lines 2694--2695 []\OT1/ptm/m/n/10.95 returns \OT1/pcr/m/n/10.95 true \OT1/ptm/m/n/10.95 if the gen-eral map-ping \OT1/pcr/m/n/10.95 f \OT1/ptm/m/n/10.95 is an in-ner au-to-mo r-phism of a semi-group; see [] [51] Underfull \hbox (badness 10000) in paragraph at lines 2709--2712 [] Underfull \hbox (badness 10000) in paragraph at lines 2735--2738 [] [52] Underfull \hbox (badness 10000) in paragraph at lines 2773--2776 [] Underfull \hbox (badness 10000) in paragraph at lines 2787--2791 []\OT1/ptm/m/n/10.95 If \OT1/pcr/m/n/10.95 autgroup \OT1/ptm/m/n/10.95 sat-is-f ies \OT1/pcr/m/n/10.95 IsAutomorphismGroupOfZeroGroup \OT1/ptm/m/n/10.95 ([][]7 .4.5[][]), then [] Underfull \hbox (badness 2189) in paragraph at lines 2787--2791 \OT1/pcr/m/n/10.95 InnerAutomorphismsAutomorphismGroup \OT1/ptm/m/n/10.95 re-tu rns the sub-group of in-ner au-to-mor-phisms in- [] Underfull \hbox (badness 10000) in paragraph at lines 2809--2812 [] [53] Underfull \hbox (badness 10000) in paragraph at lines 2836--2839 [] Underfull \hbox (badness 10000) in paragraph at lines 2871--2874 [] LaTeX Font Info: Try loading font information for OML+pcr on input line 2883 . (/usr/local/texlive/2007/texmf-dist/tex/latex/psnfss/omlpcr.fd File: omlpcr.fd ) LaTeX Font Info: Font shape `OML/pcr/m/n' in size <10.95> not available (Font) Font shape `OML/cmm/m/it' tried instead on input line 2883. [54] Underfull \hbox (badness 3568) in paragraph at lines 2900--2901 []\OT1/ptm/m/sc/10.95 Please note: \OT1/ptm/m/n/10.95 if \OT1/phv/m/n/10.95 gra pe \OT1/ptm/m/n/10.95 is not loaded, then this func-tion will not work when \OT 1/pcr/m/n/10.95 S [] Underfull \hbox (badness 10000) in paragraph at lines 2900--2901 \OT1/ptm/m/n/10.95 sat-is-fies \OT1/pcr/m/n/10.95 IsTransformationSemigroup \OT 1/ptm/m/n/10.95 (\OT1/ptm/b/n/10.95 Reference: Is-Trans-for-ma-tion-Semi-group\ OT1/ptm/m/n/10.95 ) or [] [55] Underfull \hbox (badness 10000) in paragraph at lines 2970--2973 [] Underfull \hbox (badness 2027) in paragraph at lines 2975--2976 []\OT1/pcr/m/n/10.95 AutomorphismsSemigroupInGroup \OT1/ptm/m/n/10.95 re-turns the group of au-to-mor-phisms of the trans-for- [] Underfull \hbox (badness 2617) in paragraph at lines 2975--2976 \OT1/ptm/m/n/10.95 ma-tion semi-group \OT1/pcr/m/n/10.95 S \OT1/ptm/m/n/10.95 t hat also be-long to the group \OT1/pcr/m/n/10.95 G\OT1/ptm/m/n/10.95 . If the v alue of \OT1/pcr/m/n/10.95 G \OT1/ptm/m/n/10.95 is \OT1/pcr/m/n/10.95 fail\OT1/ ptm/m/n/10.95 , then [] [56] Underfull \hbox (badness 2790) in paragraph at lines 2993--2994 \OT1/ptm/m/sc/10.95 Please note: \OT1/ptm/m/n/10.95 if \OT1/phv/m/n/10.95 grape \OT1/ptm/m/n/10.95 is not loaded, then this func-tion will not work when \OT1/ pcr/m/n/10.95 S \OT1/ptm/m/n/10.95 sat- [] Underfull \hbox (badness 10000) in paragraph at lines 2993--2994 \OT1/ptm/m/n/10.95 is-fies \OT1/pcr/m/n/10.95 IsTransformationSemigroup \OT1/pt m/m/n/10.95 (\OT1/ptm/b/n/10.95 Reference: Is-Trans-for-ma-tion-Semi-group\OT1/ ptm/m/n/10.95 ) or [] Underfull \hbox (badness 10000) in paragraph at lines 3042--3045 [] [57] Underfull \hbox (badness 10000) in paragraph at lines 3057--3060 [] Underfull \hbox (badness 10000) in paragraph at lines 3074--3077 [] Underfull \hbox (badness 10000) in paragraph at lines 3091--3094 [] Underfull \hbox (badness 10000) in paragraph at lines 3108--3111 [] [58] Underfull \hbox (badness 10000) in paragraph at lines 3126--3129 [] Underfull \hbox (badness 10000) in paragraph at lines 3151--3154 [] [59] Underfull \hbox (badness 10000) in paragraph at lines 3189--3192 [] Underfull \hbox (badness 10000) in paragraph at lines 3233--3236 [] Underfull \hbox (badness 10000) in paragraph at lines 3248--3251 [] [60] Underfull \hbox (badness 10000) in paragraph at lines 3263--3266 [] Underfull \hbox (badness 10000) in paragraph at lines 3291--3294 [] [61] Underfull \hbox (badness 10000) in paragraph at lines 3334--3337 [] [62] Underfull \hbox (badness 10000) in paragraph at lines 3369--3372 [] Underfull \hbox (badness 10000) in paragraph at lines 3404--3407 [] [63] Underfull \hbox (badness 10000) in paragraph at lines 3463--3466 [] [64] Underfull \hbox (badness 10000) in paragraph at lines 3493--3496 [] Underfull \hbox (badness 1552) in paragraph at lines 3498--3499 []\OT1/ptm/m/n/10.95 returns \OT1/pcr/m/n/10.95 true \OT1/ptm/m/n/10.95 if the ob-ject \OT1/pcr/m/n/10.95 f \OT1/ptm/m/n/10.95 is rep-re-sented as an au-to-mo r-phism of a zero group; see [] Underfull \hbox (badness 10000) in paragraph at lines 3505--3508 [] Underfull \hbox (badness 10000) in paragraph at lines 3524--3527 [] Underfull \hbox (badness 10000) in paragraph at lines 3529--3531 []\OT1/ptm/m/n/10.95 if \OT1/pcr/m/n/10.95 G \OT1/ptm/m/n/10.95 is the au-to-mo r-phism group of a sim-ple trans-for-ma-tion semi-group, then [] Underfull \hbox (badness 2277) in paragraph at lines 3529--3531 \OT1/pcr/m/n/10.95 IsomorphismAutomorphismGroupOfRMS \OT1/ptm/m/n/10.95 re-turn s a \OT1/pcr/m/n/10.95 GroupHomomorphismByImages \OT1/ptm/m/n/10.95 (\OT1/ptm/b /n/10.95 Reference: [] [65] Underfull \hbox (badness 10000) in paragraph at lines 3560--3563 [] Underfull \hbox (badness 3635) in paragraph at lines 3565--3566 \OT1/ptm/m/n/10.95 re-turns an iso-mor-phism from \OT1/pcr/m/n/10.95 G \OT1/ptm /m/n/10.95 to a per-mu-ta-tion group by com-pos-ing the re-sult \OT1/pcr/m/n/10 .95 f \OT1/ptm/m/n/10.95 of [] Underfull \hbox (badness 4686) in paragraph at lines 3569--3570 []\OT1/ptm/m/n/10.95 if \OT1/pcr/m/n/10.95 G \OT1/ptm/m/n/10.95 is a trans-for- ma-tion semi-group that sat-is-fies \OT1/pcr/m/n/10.95 IsGroupAsSemigroup \OT1/ ptm/m/n/10.95 ([][]5.2.3[][]), then [] Underfull \hbox (badness 10000) in paragraph at lines 3608--3611 [] [66] Underfull \hbox (badness 1210) in paragraph at lines 3613--3615 []\OT1/ptm/m/n/10.95 returns an iso-mor-phism to a finitely pre-sented semi-gro up from the trans-for-ma-tion semi- [] Underfull \hbox (badness 10000) in paragraph at lines 3635--3638 [] Underfull \hbox (badness 10000) in paragraph at lines 3643--3644 []\OT1/ptm/m/n/10.95 If \OT1/pcr/m/n/10.95 S \OT1/ptm/m/n/10.95 sat-is-fies \OT 1/pcr/m/n/10.95 IsSemigroup \OT1/ptm/m/n/10.95 (\OT1/ptm/b/n/10.95 Reference: I s-Semi-group\OT1/ptm/m/n/10.95 ), use the com-mand [] Underfull \hbox (badness 10000) in paragraph at lines 3662--3665 [] [67] Underfull \hbox (badness 10000) in paragraph at lines 3729--3732 [] [68] Underfull \hbox (badness 10000) in paragraph at lines 3771--3774 [] (./monoid.bbl (./monoid.brf) \tf@brf=\write7 \openout7 = `monoid.brf'. [69] Underfull \hbox (badness 7963) in paragraph at lines 39--39 []\OT1/ptm/m/n/10.95 G. Kudryavt-seva and V. Ma-zorchuk. On kisel-man's semi-g roup. 2005. [] ) (./monoid.ind [70 ] Overfull \hbox (9.78952pt too wide) in paragraph at lines 12--14 []\OT1/pcr/m/n/10.95 ConjugatorOfInnerAutomorphismOfSemigroup\OT1/ptm/m/n/10.95 , [] Underfull \hbox (badness 10000) in paragraph at lines 47--48 []\OT1/pcr/m/n/10.95 InnerAutomorphismsOfSemigroupInGroup\OT1/ptm/m/n/10.95 , [] Underfull \hbox (badness 10000) in paragraph at lines 83--85 []\OT1/pcr/m/n/10.95 IsomorphismReesMatrixSemigroupOfDClass\OT1/ptm/m/n/10.95 , [] [71 ] Underfull \hbox (badness 10000) in paragraph at lines 153--155 []\OT1/pcr/m/n/10.95 SemigroupHomomorphismByImagesOfGensNC\OT1/ptm/m/n/10.95 , [] [72]) (./monoid.aux) ) Here is how much of TeX's memory you used: 4335 strings out of 94073 62547 string characters out of 1162984 117897 words of memory out of 1500000 7167 multiletter control sequences out of 10000+50000 51712 words of font info for 95 fonts, out of 1200000 for 2000 645 hyphenation exceptions out of 8191 27i,7n,30p,1040b,622s stack positions out of 5000i,500n,6000p,200000b,5000s {/usr/local/texlive/2007/texmf-dist/fonts/enc/dvips/base/ 8r.enc}</usr/local/texlive/2007/texmf-dist/fonts/type1/bluesky/cm/cmmi10.pfb></ usr/local/texlive/2007/texmf-dist/fonts/type1/bluesky/cm/cmr10.pfb></usr/local/ texlive/2007/texmf-dist/fonts/type1/bluesky/cm/cmsy10.pfb></usr/local/texlive/2 007/texmf-dist/fonts/type1/bluesky/ams/msam10.pfb></usr/local/texlive/2007/texm f-dist/fonts/type1/urw/courier/ucrr8a.pfb></usr/local/texlive/2007/texmf-dist/f onts/type1/urw/courier/ucrro8a.pfb></usr/local/texlive/2007/texmf-dist/fonts/ty pe1/urw/helvetic/uhvb8a.pfb></usr/local/texlive/2007/texmf-dist/fonts/type1/urw /helvetic/uhvr8a.pfb></usr/local/texlive/2007/texmf-dist/fonts/type1/urw/helvet ic/uhvro8a.pfb></usr/local/texlive/2007/texmf-dist/fonts/type1/urw/times/utmb8a .pfb></usr/local/texlive/2007/texmf-dist/fonts/type1/urw/times/utmr8a.pfb></usr /local/texlive/2007/texmf-dist/fonts/type1/urw/times/utmr8a.pfb></usr/local/tex live/2007/texmf-dist/fonts/type1/urw/times/utmri8a.pfb> Output written on monoid.pdf (72 pages, 426214 bytes). PDF statistics: 1236 PDF objects out of 1440 (max. 8388607) 373 named destinations out of 1000 (max. 131072) 17 words of extra memory for PDF output out of 10000 (max. 10000000)