<html><head><title>The GAP 4 Reference Manual - Index O</title></head> <body text="#000000" bgcolor="#ffffff"> <h1>The <font face="Gill Sans,Helvetica,Arial">GAP</font> 4 Reference Manual - Index O</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>O_p(G), see PCore <a href="CHAP037.htm#I7">37.11</a> <dt>ObjByExtRep <a href="CHAP061.htm#SSEC013.7">61.13.7</a> <dt>Objects <a href="CHAP012.htm#SECT001">12.1</a> <dt>Objects and Elements <a href="CHAP012.htm">12.0</a> <dt>obsolete <a href="CHAP075.htm#I0">75.0</a> <dt>OCOneCocycles <a href="CHAP037.htm#SSEC023.3">37.23.3</a> <dt>octal character codes <a href="CHAP026.htm#I20">26.1</a> <dt>OctaveAlgebra <a href="CHAP060.htm#SSEC004.3">60.4.3</a> <dt>od <a href="CHAP004.htm#I40">4.19</a> <dt>OldGeneratorsOfPresentation <a href="CHAP046.htm#SSEC010.2">46.10.2</a> <dt>Omega <a href="CHAP037.htm#SSEC014.1">37.14.1</a> <dt>ONanScottType <a href="CHAP041.htm#SSEC004.1">41.4.1</a> <dt>OnBreak <a href="CHAP006.htm#SSEC004.3">6.4.3</a> <dt>OnBreakMessage <a href="CHAP006.htm#SSEC004.4">6.4.4</a> <dt>One <a href="CHAP030.htm#SSEC010.2">30.10.2</a> <dt>one cohomology <a href="CHAP037.htm#I9">37.23</a> <dt>OneAttr <a href="CHAP030.htm#SSEC010.2">30.10.2</a> <dt>OneCoboundaries <a href="CHAP037.htm#SSEC023.2">37.23.2</a> <dt>OneCocycles <a href="CHAP037.htm#SSEC023.1">37.23.1</a> <dt>OneFactorBound <a href="CHAP064.htm#SSEC011.8">64.11.8</a> <dt>OneImmutable <a href="CHAP030.htm#SSEC010.2">30.10.2</a> <dt>OneIrreducibleSolvableGroup <a href="CHAP048.htm#SSEC011.4">48.11.4</a> <dt>OneLibraryGroup <a href="CHAP048.htm#SSEC005.2">48.5.2</a> <dt>OneMutable <a href="CHAP030.htm#SSEC010.2">30.10.2</a> <dt>OneOfPcgs <a href="CHAP043.htm#SSEC004.6">43.4.6</a> <dt>OneOp <a href="CHAP030.htm#SSEC010.2">30.10.2</a> <dt>OnePrimitiveGroup <a href="CHAP048.htm#I4">48.5</a> <dt>OneSameMutability <a href="CHAP030.htm#SSEC010.2">30.10.2</a> <dt>OneSM <a href="CHAP030.htm#SSEC010.2">30.10.2</a> <dt>OneSmallGroup <a href="CHAP048.htm#SSEC007.3">48.7.3</a> <dt>OneTransitiveGroup <a href="CHAP048.htm#I5">48.5</a> <dt>OnIndeterminates <a href="CHAP064.htm#SSEC007.2">64.7.2</a> <dt>OnIndeterminates, as a permutation action <a href="CHAP039.htm#SSEC002.13">39.2.13</a> <dt>OnLeftInverse <a href="CHAP039.htm#SSEC002.3">39.2.3</a> <dt>OnLines <a href="CHAP039.htm#SSEC002.12">39.2.12</a> <dt>OnLines, example <a href="CHAP048.htm#I0">48.2</a> <dt>OnPairs <a href="CHAP039.htm#SSEC002.6">39.2.6</a> <dt>OnPoints <a href="CHAP039.htm#SSEC002.1">39.2.1</a> <dt>OnRight <a href="CHAP039.htm#SSEC002.2">39.2.2</a> <dt>OnSets <a href="CHAP039.htm#SSEC002.4">39.2.4</a> <dt>OnSetsDisjointSets <a href="CHAP039.htm#SSEC002.8">39.2.8</a> <dt>OnSetsSets <a href="CHAP039.htm#SSEC002.7">39.2.7</a> <dt>OnSetsTuples <a href="CHAP039.htm#SSEC002.9">39.2.9</a> <dt>OnSubspacesByCanonicalBasis <a href="CHAP039.htm#SSEC002.15">39.2.15</a> <dt>OnTuples <a href="CHAP039.htm#SSEC002.5">39.2.5</a> <dt>OnTuplesSets <a href="CHAP039.htm#SSEC002.10">39.2.10</a> <dt>OnTuplesTuples <a href="CHAP039.htm#SSEC002.11">39.2.11</a> <dt>Operation <a href="CHAP075.htm#I4">75.1</a> <dt>Operational Structure of Domains <a href="CHAP030.htm#SECT001">30.1</a> <dt>OperationAlgebraHomomorphism <a href="CHAP060.htm#SSEC009.8">60.9.8</a> <dt>OperationHomomorphism <a href="CHAP075.htm#I6">75.1</a> <dt>Operations and Attributes for Vector Spaces <a href="CHAP059.htm#SECT002">59.2</a> <dt>Operations applicable to All Streams <a href="CHAP010.htm#SECT002">10.2</a> <dt>Operations Concerning Blocks <a href="CHAP069.htm#SECT009">69.9</a> <dt>Operations for (Near-)Additive Magmas <a href="CHAP053.htm#SECT004">53.4</a> <dt>Operations for Abelian Number Fields <a href="CHAP058.htm#SECT002">58.2</a> <dt>Operations for algebraic elements <a href="CHAP065.htm#I0">65.2</a> <dt>Operations for Associative Words <a href="CHAP035.htm#SECT004">35.4</a> <dt>Operations for Associative Words by their Syllables <a href="CHAP035.htm#SECT005">35.5</a> <dt>Operations for Booleans <a href="CHAP020.htm#SECT003">20.3</a> <dt>Operations for Brauer Characters <a href="CHAP070.htm#SECT015">70.15</a> <dt>Operations for Class Functions <a href="CHAP070.htm#SECT008">70.8</a> <dt>Operations for Collections <a href="CHAP028.htm#SECT004">28.4</a> <dt>Operations for Cyclotomics <a href="CHAP018.htm#SECT001">18.1</a> <dt>Operations for Domains <a href="CHAP030.htm#SECT009">30.9</a> <dt>Operations for Finite Field Elements <a href="CHAP057.htm#SECT002">57.2</a> <dt>Operations for Finitely Presented Groups <a href="CHAP045.htm#SECT004">45.4</a> <dt>Operations for Group Homomorphisms <a href="CHAP038.htm#SECT002">38.2</a> <dt>Operations for Input Streams <a href="CHAP010.htm#SECT003">10.3</a> <dt>Operations for Lists <a href="CHAP021.htm#SECT020">21.20</a> <dt>Operations for Output Streams <a href="CHAP010.htm#SECT004">10.4</a> <dt>Operations for Pc Groups <a href="CHAP044.htm#SECT007">44.7</a> <dt>Operations for Rational Functions <a href="CHAP064.htm#SECT002">64.2</a> <dt>Operations for Special Kinds of Bases <a href="CHAP059.htm#SECT006">59.6</a> <dt>Operations for Stabilizer Chains <a href="CHAP041.htm#SECT009">41.9</a> <dt>Operations for Vector Space Bases <a href="CHAP059.htm#SECT005">59.5</a> <dt>Operations for Words <a href="CHAP034.htm#SECT003">34.3</a> <dt>Operations on elements of the algebra <a href="CHAP036.htm#SECT002">36.2</a> <dt>Operations on rewriting systems <a href="CHAP036.htm#SECT001">36.1</a> <dt>Operations to Evaluate Strings <a href="CHAP026.htm#SECT007">26.7</a> <dt>Operations to Produce or Manipulate Strings <a href="CHAP026.htm#SECT005">26.5</a> <dt>Operations which have Special Methods for Groups with Pcgs <a href="CHAP043.htm#SECT016">43.16</a> <dt>operations, for booleans <a href="CHAP020.htm#I2">20.3</a> <dt>operators <a href="CHAP004.htm#I6">4.7</a> <dt>Operators for Character Tables <a href="CHAP069.htm#SECT007">69.7</a> <dt>Operators for Matrices <a href="CHAP024.htm#SECT002">24.2</a> <dt>Operators for Row Vectors <a href="CHAP023.htm#SECT001">23.1</a> <dt>operators, arithmetic <a href="CHAP004.htm#I14">4.12</a> <dt>operators, associativity <a href="CHAP004.htm#I29">4.12</a> <dt>operators, for cyclotomics <a href="CHAP018.htm#I9">18.3</a> <dt>operators, for lists <a href="CHAP021.htm#I7">21.11</a> <dt>operators, precedence <a href="CHAP004.htm#I11">4.11</a> <a href="CHAP004.htm#I28">4.12</a> <dt>Optimization and Compiler Options <a href="CHAP073.htm#SECT012">73.12</a> <dt>options <a href="CHAP003.htm#I0">3.0</a> <a href="CHAP073.htm#I1">73.0</a> <dt>Options Stack <a href="CHAP008.htm">8.0</a> <dt>options, command line, filenames <a href="CHAP003.htm#I23">3.1</a> <dt>options, command line, internal <a href="CHAP003.htm#I35">3.2</a> <dt>options, under UNIX <a href="CHAP003.htm#I3">3.1</a> <dt>or <a href="CHAP020.htm#SSEC003.1">20.3.1</a> <dt>Orbit <a href="CHAP039.htm#SSEC003.1">39.3.1</a> <dt>Orbit Stabilizer Methods for Polycyclic Groups <a href="CHAP043.htm#SECT015">43.15</a> <dt>OrbitFusions <a href="CHAP071.htm#SSEC002.7">71.2.7</a> <dt>OrbitLength <a href="CHAP039.htm#SSEC003.4">39.3.4</a> <dt>OrbitLengths <a href="CHAP039.htm#SSEC003.5">39.3.5</a> <dt>OrbitLengthsDomain <a href="CHAP039.htm#SSEC003.6">39.3.6</a> <dt>OrbitPerms <a href="CHAP041.htm#SSEC001.1">41.1.1</a> <dt>OrbitPowerMaps <a href="CHAP071.htm#SSEC001.5">71.1.5</a> <dt>Orbits <a href="CHAP039.htm#SECT003">39.3</a> <dt>Orbits, operation/attribute <a href="CHAP039.htm#SSEC003.2">39.3.2</a> <dt>OrbitsDomain <a href="CHAP039.htm#SSEC003.3">39.3.3</a> <dt>OrbitsPerms <a href="CHAP041.htm#SSEC001.2">41.1.2</a> <dt>OrbitStabChain <a href="CHAP041.htm#SSEC009.6">41.9.6</a> <dt>OrbitStabilizer <a href="CHAP039.htm#SSEC004.1">39.4.1</a> <dt>OrbitStabilizerAlgorithm <a href="CHAP039.htm#SSEC004.3">39.4.3</a> <dt>Order <a href="CHAP030.htm#SSEC010.10">30.10.10</a> <dt>order, of a group <a href="CHAP037.htm#I0">37.1</a> <dt>Order, of a class function <a href="CHAP070.htm#I15">70.4</a> <dt>order, of a list, collection or domain <a href="CHAP028.htm#I4">28.3</a> <dt>order, of the prime residue group <a href="CHAP015.htm#I2">15.1</a> <dt>OrderedPartitions <a href="CHAP017.htm#SSEC002.17">17.2.17</a> <dt>ordering, booleans <a href="CHAP020.htm#SSEC002.2">20.2.2</a> <dt>ordering, of records <a href="CHAP027.htm#SSEC004.2">27.4.2</a> <dt>OrderingByLessThanFunctionNC <a href="CHAP029.htm#SSEC001.1">29.1.1</a> <dt>OrderingByLessThanOrEqualFunctionNC <a href="CHAP029.htm#SSEC001.2">29.1.2</a> <dt>OrderingOfRewritingSystem <a href="CHAP036.htm#SSEC001.3">36.1.3</a> <dt>OrderingOnGenerators <a href="CHAP029.htm#SSEC003.4">29.3.4</a> <dt>Orderings <a href="CHAP029.htm">29.0</a> <dt>Orderings on families of associative words <a href="CHAP029.htm#SECT003">29.3</a> <dt>OrderingsFamily <a href="CHAP029.htm#">29.0</a> <dt>OrderMod <a href="CHAP015.htm#SSEC002.1">15.2.1</a> <dt>OrderOfRewritingSystem <a href="CHAP036.htm#SSEC001.3">36.1.3</a> <dt>OrdersClassRepresentatives <a href="CHAP069.htm#SSEC008.5">69.8.5</a> <dt>OrdersTom <a href="CHAP068.htm#SSEC007.2">68.7.2</a> <dt>Ordinal <a href="CHAP026.htm#SSEC007.2">26.7.2</a> <dt>ordinary character <a href="CHAP070.htm#I19">70.8</a> <dt>OrdinaryCharacterTable <a href="CHAP069.htm#SSEC008.4">69.8.4</a> <dt>Orthogonal Embeddings <a href="CHAP025.htm#SECT006">25.6</a> <dt>OrthogonalComponents <a href="CHAP070.htm#SSEC011.4">70.11.4</a> <dt>OrthogonalEmbeddings <a href="CHAP025.htm#SSEC006.1">25.6.1</a> <dt>OrthogonalEmbeddingsSpecialDimension <a href="CHAP070.htm#SSEC010.6">70.10.6</a> <dt>OSX <a href="CHAP073.htm#I6">73.14</a> <dt>Other Filters <a href="CHAP013.htm#SECT008">13.8</a> <dt>Other Operations Applicable to any Object <a href="CHAP012.htm#SECT008">12.8</a> <dt>Other Operations for Character Tables <a href="CHAP069.htm#SECT010">69.10</a> <dt>Other Operations for Tables of Marks <a href="CHAP068.htm#SECT009">68.9</a> <dt>output, suppressing <a href="CHAP006.htm#I6">6.1</a> <dt>OutputLogTo <a href="CHAP009.htm#SSEC007.9">9.7.9</a> <dt>OutputLogTo, for streams <a href="CHAP010.htm#SSEC004.7">10.4.7</a> <dt>OutputLogTo, stop logging output <a href="CHAP009.htm#SSEC007.10">9.7.10</a> <dt>OutputTextFile <a href="CHAP010.htm#SSEC005.2">10.5.2</a> <dt>OutputTextNone <a href="CHAP010.htm#SSEC009.2">10.9.2</a> <dt>OutputTextString <a href="CHAP010.htm#SSEC007.2">10.7.2</a> <dt>OutputTextUser <a href="CHAP010.htm#SSEC006.2">10.6.2</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>
