<html><head><title>The GAP 4 Reference Manual - Index F</title></head> <body text="#000000" bgcolor="#ffffff"> <h1>The <font face="Gill Sans,Helvetica,Arial">GAP</font> 4 Reference Manual - Index F</h1> <p> <a href="theindex.htm">_</A> <a href="indxA.htm">A</A> <a href="indxB.htm">B</A> <a href="indxC.htm">C</A> <a href="indxD.htm">D</A> <a href="indxE.htm">E</A> <a href="indxF.htm">F</A> <a href="indxG.htm">G</A> <a href="indxH.htm">H</A> <a href="indxI.htm">I</A> <a href="indxJ.htm">J</A> <a href="indxK.htm">K</A> <a href="indxL.htm">L</A> <a href="indxM.htm">M</A> <a href="indxN.htm">N</A> <a href="indxO.htm">O</A> <a href="indxP.htm">P</A> <a href="indxQ.htm">Q</A> <a href="indxR.htm">R</A> <a href="indxS.htm">S</A> <a href="indxT.htm">T</A> <a href="indxU.htm">U</A> <a href="indxV.htm">V</A> <a href="indxW.htm">W</A> <a href="indxX.htm">X</A> <a href="indxY.htm">Y</A> <a href="indxZ.htm">Z</A> <dt>f_N <a href="CHAP018.htm#I15">18.4</a> <dt>Factor Groups <a href="CHAP037.htm#SECT018">37.18</a> <dt>Factor Groups of Polycyclic Groups - Modulo Pcgs <a href="CHAP043.htm#SECT009">43.9</a> <dt>Factor Groups of Polycyclic Groups in their Own Representation <a href="CHAP043.htm#SECT010">43.10</a> <dt>FactorCosetAction <a href="CHAP039.htm#SSEC007.1">39.7.1</a> <dt>FactorCosetAction, for fp groups <a href="CHAP045.htm#SSEC005.3">45.5.3</a> <dt>FactorCosetOperation <a href="CHAP045.htm#SSEC005.3">45.5.3</a> <dt>FactorFreeSemigroupByRelations <a href="CHAP051.htm#SSEC001.2">51.1.2</a> <dt>FactorGroup <a href="CHAP037.htm#SSEC018.2">37.18.2</a> <dt>FactorGroupFpGroupByRels <a href="CHAP045.htm#SSEC001.2">45.1.2</a> <dt>FactorGroupNC <a href="CHAP037.htm#SSEC018.2">37.18.2</a> <dt>FactorGroupNormalSubgroupClasses <a href="CHAP069.htm#SSEC021.4">69.21.4</a> <dt>FactorGroupTom <a href="CHAP068.htm#SSEC009.11">68.9.11</a> <dt>Factorial <a href="CHAP017.htm#SSEC001.1">17.1.1</a> <dt>Factorization <a href="CHAP037.htm#SSEC005.2">37.5.2</a> <dt>factorization <a href="CHAP037.htm#I1">37.5</a> <dt>Factors <a href="CHAP054.htm#SSEC005.8">54.5.8</a> <dt>Factors, of univariate polynomial <a href="CHAP064.htm#SSEC010.1">64.10.1</a> <dt>FactorsInt <a href="CHAP014.htm#SSEC003.6">14.3.6</a> <dt>FactorsOfDirectProduct <a href="CHAP069.htm#SSEC018.2">69.18.2</a> <dt>FactorsSquarefree <a href="CHAP064.htm#SSEC010.2">64.10.2</a> <dt>Fail <a href="CHAP020.htm#SECT001">20.1</a> <dt>fail <a href="CHAP020.htm#SSEC001.1">20.1.1</a> <dt>FaithfulModule <a href="CHAP060.htm#SSEC010.20">60.10.20</a> <dt>FaithfulModule, for Lie algebras <a href="CHAP061.htm#SSEC012.1">61.12.1</a> <dt>Families <a href="CHAP013.htm#SECT001">13.1</a> <dt>FamiliesOfGeneralMappingsAndRanges <a href="CHAP031.htm#SSEC013.5">31.13.5</a> <dt>FamiliesOfRows <a href="CHAP069.htm#SSEC020.5">69.20.5</a> <dt>FamilyForOrdering <a href="CHAP029.htm#SSEC002.4">29.2.4</a> <dt>FamilyObj <a href="CHAP013.htm#SSEC001.1">13.1.1</a> <dt>FamilyPcgs <a href="CHAP044.htm#SSEC001.1">44.1.1</a> <dt>FamilyRange <a href="CHAP031.htm#SSEC013.3">31.13.3</a> <dt>FamilySource <a href="CHAP031.htm#SSEC013.4">31.13.4</a> <dt>FAQ <a href="CHAP073.htm#I3">73.9</a> <dt>features, under UNIX <a href="CHAP003.htm#I1">3.1</a> <dt>fi <a href="CHAP004.htm#I31">4.16</a> <dt>Fibonacci <a href="CHAP017.htm#SSEC003.1">17.3.1</a> <dt>Fibonacci and Lucas Sequences <a href="CHAP017.htm#SECT003">17.3</a> <dt>Field <a href="CHAP056.htm#SSEC001.3">56.1.3</a> <dt>field homomorphisms, Frobenius <a href="CHAP057.htm#I3">57.4</a> <dt>FieldExtension <a href="CHAP056.htm#SSEC002.9">56.2.9</a> <dt>FieldOfMatrixGroup <a href="CHAP042.htm#SSEC001.3">42.1.3</a> <dt>FieldOverItselfByGenerators <a href="CHAP056.htm#SSEC002.2">56.2.2</a> <dt>fields <a href="CHAP056.htm#I0">56.0</a> <dt>Fields and Division Rings <a href="CHAP056.htm">56.0</a> <dt>File Access <a href="CHAP009.htm#SECT006">9.6</a> <dt>File Operations <a href="CHAP009.htm#SECT007">9.7</a> <dt>File Streams <a href="CHAP010.htm#SECT005">10.5</a> <dt>FileDescriptorOfStream <a href="CHAP010.htm#SSEC002.2">10.2.2</a> <dt>Filename <a href="CHAP009.htm#SECT004">9.4</a> <a href="CHAP009.htm#SSEC004.1">9.4.1</a> <dt>Files and Filenames <a href="CHAP009.htm">9.0</a> <dt>Filtered <a href="CHAP021.htm#SSEC020.18">21.20.18</a> <dt>Filters <a href="CHAP013.htm#SECT002">13.2</a> <dt>Filters Controlling the Arithmetic Behaviour of Lists <a href="CHAP021.htm#SECT012">21.12</a> <dt>Finding Positions in Lists <a href="CHAP021.htm#SECT016">21.16</a> <dt>Finding Submodules <a href="CHAP067.htm#SECT006">67.6</a> <dt>FindSl2 <a href="CHAP061.htm#SSEC009.7">61.9.7</a> <dt>Finish Installation and Cleanup <a href="CHAP073.htm#SECT007">73.7</a> <dt>Finite Field Elements <a href="CHAP057.htm#SECT001">57.1</a> <dt>Finite Fields <a href="CHAP057.htm">57.0</a> <dt>Finite Perfect Groups <a href="CHAP048.htm#SECT008">48.8</a> <dt>Finitely Presented Algebras <a href="CHAP062.htm">62.0</a> <dt>Finitely Presented Groups <a href="CHAP045.htm">45.0</a> <dt>Finitely Presented Lie Algebras <a href="CHAP061.htm#SECT011">61.11</a> <dt>Finitely presented monoids <a href="CHAP051.htm#SECT004">51.4</a> <dt>Finitely Presented Semigroups and Monoids <a href="CHAP051.htm">51.0</a> <dt>finiteness test, for a list or collection <a href="CHAP028.htm#I2">28.3</a> <dt>First <a href="CHAP021.htm#SSEC020.20">21.20.20</a> <dt>FittingSubgroup <a href="CHAP037.htm#SSEC012.5">37.12.5</a> <dt>Flat <a href="CHAP021.htm#SSEC020.6">21.20.6</a> <dt>flush character <a href="CHAP026.htm#I18">26.1</a> <dt>For <a href="CHAP004.htm#SECT019">4.19</a> <dt>for loop <a href="CHAP004.htm#SSEC019.1">4.19.1</a> <dt>ForAll <a href="CHAP021.htm#SSEC020.21">21.20.21</a> <dt>ForAny <a href="CHAP021.htm#SSEC020.22">21.20.22</a> <dt>FpElmComparisonMethod <a href="CHAP045.htm#SSEC002.3">45.2.3</a> <dt>FpGroupPresentation <a href="CHAP046.htm#SSEC001.4">46.1.4</a> <dt>FpGrpMonSmgOfFpGrpMonSmgElement <a href="CHAP051.htm#">51.0</a> <dt>FpLieAlgebraByCartanMatrix <a href="CHAP061.htm#SSEC011.1">61.11.1</a> <dt>Frame <a href="CHAP070.htm#I38">70.11</a> <dt>FrattiniSubgroup <a href="CHAP037.htm#SSEC012.6">37.12.6</a> <dt>FrattiniSubgroup, for groups with pcgs <a href="CHAP043.htm#I6">43.16</a> <dt>Free Groups, Monoids and Semigroups <a href="CHAP035.htm#SECT002">35.2</a> <dt>Free Magma Rings <a href="CHAP063.htm#SECT001">63.1</a> <dt>Free Magmas <a href="CHAP034.htm#SECT004">34.4</a> <dt>Free Modules <a href="CHAP055.htm#SECT003">55.3</a> <dt>Free Products <a href="CHAP047.htm#SECT005">47.5</a> <dt>FreeAlgebra <a href="CHAP060.htm#SSEC002.1">60.2.1</a> <dt>FreeAlgebraWithOne <a href="CHAP060.htm#SSEC002.2">60.2.2</a> <dt>FreeAssociativeAlgebra <a href="CHAP060.htm#SSEC002.3">60.2.3</a> <dt>FreeAssociativeAlgebraWithOne <a href="CHAP060.htm#SSEC002.4">60.2.4</a> <dt>FreeGeneratorsOfFpGroup <a href="CHAP045.htm#SSEC003.2">45.3.2</a> <dt>FreeGeneratorsOfFpSemigroup <a href="CHAP051.htm#SSEC003.2">51.3.2</a> <dt>FreeGeneratorsOfWholeGroup <a href="CHAP045.htm#SSEC003.2">45.3.2</a> <dt>FreeGroup <a href="CHAP035.htm#SSEC002.1">35.2.1</a> <dt>FreeGroupOfFpGroup <a href="CHAP045.htm#SSEC003.1">45.3.1</a> <dt>FreeLeftModule <a href="CHAP055.htm#SSEC003.2">55.3.2</a> <dt>FreeLieAlgebra <a href="CHAP061.htm#SSEC002.3">61.2.3</a> <dt>FreeMagma <a href="CHAP034.htm#SSEC004.1">34.4.1</a> <dt>FreeMagmaRing <a href="CHAP063.htm#SSEC001.1">63.1.1</a> <dt>FreeMagmaWithOne <a href="CHAP034.htm#SSEC004.2">34.4.2</a> <dt>FreeMonoid <a href="CHAP050.htm#">50.0</a> <a href="CHAP050.htm#">50.0</a> <a href="CHAP050.htm#">50.0</a> <a href="CHAP050.htm#">50.0</a> <a href="CHAP050.htm#">50.0</a> <dt>FreeMonoid, with example <a href="CHAP035.htm#SSEC002.3">35.2.3</a> <dt>FreeMonoidOfRewritingSystem <a href="CHAP051.htm#SSEC005.7">51.5.7</a> <dt>FreeProduct <a href="CHAP047.htm#SSEC005.1">47.5.1</a> <dt>FreeSemigroup <a href="CHAP035.htm#SSEC002.4">35.2.4</a> <dt>FreeSemigroup, with examples <a href="CHAP049.htm#">49.0</a> <a href="CHAP049.htm#">49.0</a> <a href="CHAP049.htm#">49.0</a> <a href="CHAP049.htm#">49.0</a> <a href="CHAP049.htm#">49.0</a> <dt>FreeSemigroupOfFpSemigroup <a href="CHAP051.htm#SSEC003.1">51.3.1</a> <dt>FreeSemigroupOfRewritingSystem <a href="CHAP051.htm#SSEC005.6">51.5.6</a> <dt>Frobenius automorphism <a href="CHAP057.htm#I6">57.4</a> <dt>FrobeniusAutomorphism <a href="CHAP057.htm#SECT004">57.4</a> <a href="CHAP057.htm#SSEC004.1">57.4.1</a> <dt>FrobeniusCharacterValue <a href="CHAP070.htm#SSEC015.1">70.15.1</a> <dt>FullMatrixAlgebra <a href="CHAP060.htm#SSEC004.4">60.4.4</a> <dt>FullMatrixAlgebraCentralizer <a href="CHAP060.htm#SSEC008.15">60.8.15</a> <dt>FullMatrixLieAlgebra <a href="CHAP061.htm#SSEC002.4">61.2.4</a> <dt>FullMatrixModule <a href="CHAP055.htm#SSEC003.12">55.3.12</a> <dt>FullMatrixSpace <a href="CHAP059.htm#SSEC008.5">59.8.5</a> <dt>FullRowModule <a href="CHAP055.htm#SSEC003.10">55.3.10</a> <dt>FullRowSpace <a href="CHAP059.htm#SSEC008.4">59.8.4</a> <dt>FullTransformationSemigroup <a href="CHAP049.htm#SSEC001.5">49.1.5</a> <dt>Function <a href="CHAP004.htm#SECT022">4.22</a> <dt>function <a href="CHAP004.htm#SSEC022.1">4.22.1</a> <dt>function call <a href="CHAP004.htm#SSEC010.1">4.10.1</a> <dt>function call, with arguments <a href="CHAP004.htm#SSEC010.1">4.10.1</a> <dt>function call, with options <a href="CHAP004.htm#SSEC010.2">4.10.2</a> <dt>Function Calls <a href="CHAP004.htm#SECT010">4.10</a> <dt>Function that Modify Boolean Lists <a href="CHAP022.htm#SECT003">22.3</a> <dt>Function Types <a href="CHAP005.htm#SECT004">5.4</a> <dt>FunctionAction <a href="CHAP039.htm#SSEC011.4">39.11.4</a> <dt>FunctionOperation <a href="CHAP075.htm#I7">75.1</a> <dt>Functions <a href="CHAP005.htm">5.0</a> <dt>functions <a href="CHAP005.htm#I0">5.0</a> <a href="CHAP031.htm#I0">31.0</a> <dt>Functions for Coding Theory <a href="CHAP023.htm#SECT005">23.5</a> <dt>Functions for GAP Packages <a href="CHAP074.htm#SECT003">74.3</a> <dt>Functions that do nothing <a href="CHAP005.htm#SECT003">5.3</a> <dt>functions, definition by arrow notation <a href="CHAP004.htm#I52">4.22</a> <dt>functions, definition of <a href="CHAP004.htm#I43">4.22</a> <dt>functions, recursive <a href="CHAP004.htm#I47">4.22</a> <dt>functions, with a variable number of arguments <a href="CHAP004.htm#I9">4.10</a> <a href="CHAP004.htm#I50">4.22</a> <dt>FunctionsFamily <a href="CHAP005.htm#SSEC004.3">5.4.3</a> <dt>FusionCharTableTom <a href="CHAP068.htm#SSEC012.1">68.12.1</a> <dt>FusionConjugacyClasses <a href="CHAP071.htm#SSEC002.1">71.2.1</a> <dt>FusionConjugacyClassesOp <a href="CHAP071.htm#SSEC002.1">71.2.1</a> <dt>fusions <a href="CHAP071.htm#I3">71.2</a> <dt>FusionsAllowedByRestrictions <a href="CHAP071.htm#SSEC005.4">71.5.4</a> <dt>FusionsTom <a href="CHAP068.htm#SSEC007.6">68.7.6</a> </dl><p> [<a href="../index.htm">Top</a>] [<a href="chapters.htm">Up</a>]<p> <P> <font face="Gill Sans,Helvetica,Arial">GAP 4 manual<br>December 2008 </font></body></html>
