<html><head><title>CRISP : a GAP 4 package - Index </title></head> <body text="#000000" bgcolor="#ffffff"> <h1><font face="Gill Sans,Helvetica,Arial">CRISP</font> : a <font face="Gill Sans,Helvetica,Arial">GAP</font> 4 package - Index </h1> <p> <a href="#idxA">A</A> <a href="#idxB">B</A> <a href="#idxC">C</A> <a href="#idxD">D</A> <a href="#idxE">E</A> <a href="#idxF">F</A> <a href="#idxG">G</A> <a href="#idxH">H</A> <a href="#idxI">I</A> <a href="#idxL">L</A> <a href="#idxM">M</A> <a href="#idxN">N</A> <a href="#idxO">O</A> <a href="#idxP">P</A> <a href="#idxQ">Q</A> <a href="#idxR">R</A> <a href="#idxS">S</A> <a href="#idxT">T</A> <a href="#idxU">U</A> <a href="#idxV">V</A> <H2><A NAME="idxA">A</A></H2> <dl> <dt>abelian groups of bounded exponent, class of <a href="CHAP006.htm#I10">6.1</a> <dt>abelian groups, class of <a href="CHAP006.htm#I7">6.1</a> <dt>AbelianGroups <a href="CHAP006.htm#I6">6.1</a> <dt>AbelianGroupsOfExponent <a href="CHAP006.htm#SSEC001.5">6.1.5</a> <dt>AbelianMinimalNormalSubgroups <a href="CHAP005.htm#SSEC005.7">5.5.7</a> <dt>AbelianSocle <a href="CHAP005.htm#SSEC005.2">5.5.2</a> <dt>AbelianSocleComponents <a href="CHAP005.htm#SSEC005.4">5.5.4</a> <dt>Additional attributes for primitive solvable groups <a href="CHAP004.htm#SECT003">4.3</a> <dt>Additional properties of group classes <a href="CHAP003.htm#SECT003">3.3</a> <dt>AllInvariantSubgroupsWithNProperty <a href="CHAP005.htm#SSEC006.2">5.6.2</a> <dt>AllInvariantSubgroupsWithQProperty <a href="CHAP004.htm#SSEC007.2">4.7.2</a> <dt>AllNormalSubgroupsWithNProperty <a href="CHAP005.htm#SSEC006.3">5.6.3</a> <dt>AllNormalSubgroupsWithQProperty <a href="CHAP004.htm#SSEC007.4">4.7.4</a> <dt>Attributes and operations for Fitting classes and Fitting sets <a href="CHAP005.htm#SECT004">5.4</a> <dt>Attributes and operations for formations <a href="CHAP004.htm#SECT005">4.5</a> <dt>Attributes and operations for Schunck classes <a href="CHAP004.htm#SECT002">4.2</a> <dt>Attributes of group classes <a href="CHAP003.htm#SECT004">3.4</a> <dt>attributes, of Fitting classes <a href="CHAP005.htm#I6">5.4</a> <dt>attributes, of Fitting sets <a href="CHAP005.htm#I5">5.4</a> <dt>attributes, of formation <a href="CHAP004.htm#I10">4.5</a> <dt>attributes, of group classes <a href="CHAP003.htm#I9">3.4</a> <dt>attributes, of primitive solvable group <a href="CHAP004.htm#I6">4.3</a> <dt>attributes, of Schunck class <a href="CHAP004.htm#I3">4.2</a> </dl><p> <H2><A NAME="idxB">B</A></H2> <dl> <dt>Basis <a href="CHAP004.htm#SSEC002.2">4.2.2</a> <dt>Boundary <a href="CHAP004.htm#SSEC002.1">4.2.1</a> <dt>BoundaryFunction <a href="CHAP004.htm#SSEC002.5">4.2.5</a> </dl><p> <H2><A NAME="idxC">C</A></H2> <dl> <dt>Carter subgroup <a href="CHAP006.htm#I13">6.2</a> <dt>Characteristic <a href="CHAP003.htm#SSEC004.1">3.4.1</a> <dt>CharacteristicSubgroups <a href="CHAP004.htm#SSEC006.2">4.6.2</a> <dt>Class <a href="CHAP002.htm#SSEC001.2">2.1.2</a> <dt>class, of all abelian groups <a href="CHAP006.htm#SSEC001.4">6.1.4</a> <a href="CHAP006.htm#I8">6.1</a> <dt>class, of all abelian groups of bounded exponent <a href="CHAP006.htm#I9">6.1</a> <dt>class, of all nilpotent groups <a href="CHAP006.htm#SSEC001.2">6.1.2</a> <a href="CHAP006.htm#I3">6.1</a> <dt>class, of all p-groups <a href="CHAP006.htm#I12">6.1</a> <dt>class, of all pi-groups <a href="CHAP006.htm#I11">6.1</a> <dt>class, of all supersolvable groups <a href="CHAP006.htm#SSEC001.3">6.1.3</a> <a href="CHAP006.htm#I5">6.1</a> <dt>class, of all trivial groups <a href="CHAP006.htm#SSEC001.1">6.1.1</a> <a href="CHAP006.htm#I1">6.1</a> <dt>classes, creating <a href="CHAP002.htm#I0">2.1</a> <dt>classes, properties of <a href="CHAP002.htm#I3">2.2</a> <dt>closure properties, of group classes <a href="CHAP003.htm#I1">3.2</a> <dt>comparison, for classes <a href="CHAP002.htm#SSEC001.8">2.1.8</a> <dt>Complement <a href="CHAP002.htm#SSEC003.1">2.3.1</a> <dt>ContainsTrivialGroup <a href="CHAP003.htm#SSEC002.2">3.2.2</a> <dt>CoveringSubgroup <a href="CHAP004.htm#SSEC002.4">4.2.4</a> <dt>Creating Fitting classes <a href="CHAP005.htm#SECT001">5.1</a> <dt>Creating Fitting formations <a href="CHAP005.htm#SECT002">5.2</a> <dt>Creating Fitting sets <a href="CHAP005.htm#SECT003">5.3</a> <dt>Creating formations <a href="CHAP004.htm#SECT004">4.4</a> <dt>Creating group classes <a href="CHAP003.htm#SECT001">3.1</a> <dt>Creating Schunck classes <a href="CHAP004.htm#SECT001">4.1</a> <dt>Creating set theoretical classes <a href="CHAP002.htm#SECT001">2.1</a> <dt>CRISP <a href="CHAP001.htm#I0">1.0</a> </dl><p> <H2><A NAME="idxD">D</A></H2> <dl> <dt>Difference <a href="CHAP002.htm#SSEC003.4">2.3.4</a> <dt>Display, for classes <a href="CHAP002.htm#SSEC001.5">2.1.5</a> </dl><p> <H2><A NAME="idxE">E</A></H2> <dl> <dt>element test, for classes <a href="CHAP002.htm#SSEC001.6">2.1.6</a> <dt>equality, for classes <a href="CHAP002.htm#SSEC001.7">2.1.7</a> <dt>Examples of group classes <a href="CHAP006.htm">6.0</a> </dl><p> <H2><A NAME="idxF">F</A></H2> <dl> <dt>factor groups, with properties inherited by factor groups <a href="CHAP004.htm#I14">4.7</a> <dt>Fitting classes and Fitting sets <a href="CHAP005.htm">5.0</a> <dt>Fitting classes, attributes of <a href="CHAP005.htm#I12">5.4</a> <dt>Fitting classes, creating <a href="CHAP005.htm#I0">5.1</a> <dt>Fitting classes, creating Fitting formations <a href="CHAP005.htm#I3">5.2</a> <dt>Fitting classes, operations for <a href="CHAP005.htm#I10">5.4</a> <dt>Fitting formations, creating <a href="CHAP005.htm#I1">5.2</a> <dt>Fitting sets, attributes of <a href="CHAP005.htm#I11">5.4</a> <dt>Fitting sets, creating <a href="CHAP005.htm#I4">5.3</a> <dt>Fitting sets, operations for <a href="CHAP005.htm#I9">5.4</a> <dt>FittingClass <a href="CHAP005.htm#SSEC001.1">5.1.1</a> <dt>FittingFormation <a href="CHAP005.htm#SSEC002.1">5.2.1</a> <dt>FittingFormationProduct <a href="CHAP004.htm#SSEC004.4">4.4.4</a> <dt>FittingProduct <a href="CHAP005.htm#SSEC001.2">5.1.2</a> <dt>FittingSet <a href="CHAP005.htm#SSEC003.2">5.3.2</a> <dt>FormationProduct <a href="CHAP004.htm#SSEC004.3">4.4.3</a> <dt>formations, attributes for <a href="CHAP004.htm#I8">4.5</a> <dt>formations, creating <a href="CHAP004.htm#I7">4.4</a> <dt>formations, creating Fitting formations <a href="CHAP005.htm#I2">5.2</a> <dt>formations, operations for <a href="CHAP004.htm#I9">4.5</a> <dt>Functions for minimal normal subgroups and the socle <a href="CHAP005.htm#SECT005">5.5</a> <dt>Functions for normal and characteristic subgroups <a href="CHAP004.htm#SECT006">4.6</a> </dl><p> <H2><A NAME="idxG">G</A></H2> <dl> <dt>Generic group classes <a href="CHAP003.htm">3.0</a> <dt>group classes, attributes for <a href="CHAP003.htm#I8">3.4</a> <dt>group classes, closure properties of <a href="CHAP003.htm#I2">3.2</a> <dt>group classes, creation <a href="CHAP003.htm#I0">3.1</a> <dt>group classes, properties of <a href="CHAP003.htm#I3">3.3</a> <dt>GroupClass <a href="CHAP003.htm#SSEC001.1">3.1.1</a> </dl><p> <H2><A NAME="idxH">H</A></H2> <dl> <dt>HasIsFittingClass <a href="CHAP003.htm#SSEC003.1">3.3.1</a> <dt>HasIsFittingFormation <a href="CHAP003.htm#SSEC003.10">3.3.10</a> <dt>HasIsFormation <a href="CHAP003.htm#I5">3.3</a> <dt>HasIsOrdinaryFormation <a href="CHAP003.htm#SSEC003.4">3.3.4</a> <dt>HasIsSaturatedFittingFormation <a href="CHAP003.htm#SSEC003.13">3.3.13</a> <dt>HasIsSaturatedFormation <a href="CHAP003.htm#SSEC003.7">3.3.7</a> </dl><p> <H2><A NAME="idxI">I</A></H2> <dl> <dt>ImageFittingSet <a href="CHAP005.htm#SSEC003.3">5.3.3</a> <dt>in, for classes <a href="CHAP002.htm#I1">2.1</a> <dt>Injector <a href="CHAP005.htm#SSEC004.2">5.4.2</a> <dt>InjectorFunction <a href="CHAP005.htm#SSEC004.4">5.4.4</a> <dt>Intersection, of classes <a href="CHAP002.htm#SSEC003.2">2.3.2</a> <dt>Intersection, of Fitting sets <a href="CHAP005.htm#SSEC003.5">5.3.5</a> <dt>Intersection, of group classes <a href="CHAP003.htm#SSEC001.2">3.1.2</a> <dt>INTERSECTIONnoexpand_LIMIT <a href="CHAP002.htm#I6">2.3</a> <dt>Introduction <a href="CHAP001.htm">1.0</a> <dt>invariant normal subgroups, with properties inherited by normal subgroups <a href="CHAP005.htm#I15">5.6</a> <dt>invariant normal subgroups, with properties inherited by normal subgroups above <a href="CHAP004.htm#I13">4.7</a> <dt>IsClass <a href="CHAP002.htm#SSEC001.1">2.1.1</a> <dt>IsDirectProductClosed <a href="CHAP003.htm#SSEC002.8">3.2.8</a> <dt>IsEmpty, for classes <a href="CHAP002.htm#SSEC002.1">2.2.1</a> <dt>IsFittingClass <a href="CHAP003.htm#SSEC003.2">3.3.2</a> <dt>IsFittingFormation <a href="CHAP003.htm#SSEC003.11">3.3.11</a> <dt>IsFittingSet <a href="CHAP005.htm#SSEC003.1">5.3.1</a> <dt>IsFormation <a href="CHAP003.htm#I6">3.3</a> <dt>IsGroupClass <a href="CHAP003.htm#SSEC002.1">3.2.1</a> <dt>IsNormalProductClosed <a href="CHAP003.htm#SSEC002.7">3.2.7</a> <dt>IsNormalSubgroupClosed <a href="CHAP003.htm#SSEC002.4">3.2.4</a> <dt>IsOrdinaryFormation <a href="CHAP003.htm#SSEC003.5">3.3.5</a> <dt>IsPrimitiveSolvable <a href="CHAP004.htm#SSEC003.1">4.3.1</a> <dt>IsQuotientClosed <a href="CHAP003.htm#SSEC002.5">3.2.5</a> <dt>IsResiduallyClosed <a href="CHAP003.htm#SSEC002.6">3.2.6</a> <dt>IsSaturated <a href="CHAP003.htm#SSEC002.10">3.2.10</a> <dt>IsSaturatedFittingFormation <a href="CHAP003.htm#SSEC003.14">3.3.14</a> <dt>IsSaturatedFormation <a href="CHAP003.htm#SSEC003.8">3.3.8</a> <dt>IsSchunckClass <a href="CHAP003.htm#SSEC002.9">3.2.9</a> <dt>IsSubgroupClosed <a href="CHAP003.htm#SSEC002.3">3.2.3</a> </dl><p> <H2><A NAME="idxL">L</A></H2> <dl> <dt>Lattice operations for classes <a href="CHAP002.htm#SECT003">2.3</a> <dt>lattice operations, for classes <a href="CHAP002.htm#I5">2.3</a> <dt>LocalDefinitionFunction <a href="CHAP004.htm#SSEC005.3">4.5.3</a> <dt>Low level functions for normal subgroups related to radicals <a href="CHAP005.htm#SECT006">5.6</a> <dt>Low level functions for normal subgroups related to residuals <a href="CHAP004.htm#SECT007">4.7</a> </dl><p> <H2><A NAME="idxM">M</A></H2> <dl> <dt>MemberFunction <a href="CHAP002.htm#SSEC002.2">2.2.2</a> <dt>membership test, for classes <a href="CHAP002.htm#I2">2.1</a> <dt>minimal normal subgroups <a href="CHAP005.htm#I13">5.5</a> </dl><p> <H2><A NAME="idxN">N</A></H2> <dl> <dt>nilpotent groups, class of <a href="CHAP006.htm#I2">6.1</a> <dt>NilpotentProjector <a href="CHAP006.htm#SSEC002.1">6.2.1</a> <dt>normal subgroups, with properties inherited by normal subgroups <a href="CHAP005.htm#I14">5.6</a> <dt>normal subgroups, with properties inherited by normal subgroups above <a href="CHAP004.htm#I12">4.7</a> <dt>NormalSubgroups <a href="CHAP004.htm#SSEC006.1">4.6.1</a> </dl><p> <H2><A NAME="idxO">O</A></H2> <dl> <dt>OneInvariantSubgroupMaxWrtNProperty <a href="CHAP005.htm#SSEC006.1">5.6.1</a> <dt>OneInvariantSubgroupMinWrtQProperty <a href="CHAP004.htm#SSEC007.1">4.7.1</a> <dt>OneNormalSubgroupMinWrtQProperty <a href="CHAP004.htm#SSEC007.3">4.7.3</a> <dt>OneNormalSubgroupWithNProperty <a href="CHAP005.htm#SSEC006.3">5.6.3</a> <dt>operations, for Fitting classes <a href="CHAP005.htm#I8">5.4</a> <dt>operations, for Fitting sets <a href="CHAP005.htm#I7">5.4</a> <dt>operations, for formation <a href="CHAP004.htm#I11">4.5</a> <dt>operations, for Schunck class, <a href="CHAP004.htm#I4">4.2</a> <dt>OrdinaryFormation <a href="CHAP004.htm#SSEC004.1">4.4.1</a> </dl><p> <H2><A NAME="idxP">P</A></H2> <dl> <dt>PGroups <a href="CHAP006.htm#SSEC001.7">6.1.7</a> <dt>PiGroups <a href="CHAP006.htm#SSEC001.6">6.1.6</a> <dt>Pre-defined group classes <a href="CHAP006.htm#SECT001">6.1</a> <dt>Pre-defined projector functions <a href="CHAP006.htm#SECT002">6.2</a> <dt>Pre-defined sets of primes <a href="CHAP006.htm#SECT003">6.3</a> <dt>PreImageFittingSet <a href="CHAP005.htm#SSEC003.4">5.3.4</a> <dt>primes, set of all <a href="CHAP006.htm#I14">6.3</a> <dt>primitive solvable group, attributes of <a href="CHAP004.htm#I5">4.3</a> <dt>Print, for classes <a href="CHAP002.htm#SSEC001.4">2.1.4</a> <dt>Projector <a href="CHAP004.htm#SSEC002.3">4.2.3</a> <dt>ProjectorFunction <a href="CHAP004.htm#SSEC002.6">4.2.6</a> <dt>Properties of classes <a href="CHAP002.htm#SECT002">2.2</a> <dt>Properties of group classes <a href="CHAP003.htm#SECT002">3.2</a> <dt>properties, of classes <a href="CHAP002.htm#I4">2.2</a> <dt>properties, of group classes <a href="CHAP003.htm#I4">3.3</a> <dt>PSocle <a href="CHAP005.htm#SSEC005.5">5.5.5</a> <dt>PSocleComponents <a href="CHAP005.htm#SSEC005.6">5.5.6</a> </dl><p> <H2><A NAME="idxQ">Q</A></H2> <dl> <dt>quotient groups, with properties inherited by quotients <a href="CHAP004.htm#I15">4.7</a> </dl><p> <H2><A NAME="idxR">R</A></H2> <dl> <dt>Radical <a href="CHAP005.htm#SSEC004.1">5.4.1</a> <dt>RadicalFunction <a href="CHAP005.htm#SSEC004.3">5.4.3</a> <dt>Residual <a href="CHAP004.htm#SSEC005.1">4.5.1</a> <dt>ResidualFunction <a href="CHAP004.htm#SSEC005.2">4.5.2</a> <dt>Residuum <a href="CHAP004.htm#SSEC005.1">4.5.1</a> </dl><p> <H2><A NAME="idxS">S</A></H2> <dl> <dt>SaturatedFittingFormation <a href="CHAP005.htm#SSEC002.2">5.2.2</a> <dt>SaturatedFormation <a href="CHAP004.htm#SSEC004.2">4.4.2</a> <dt>Schunck class, attributes of <a href="CHAP004.htm#I1">4.2</a> <dt>Schunck class, creating <a href="CHAP004.htm#I0">4.1</a> <dt>Schunck class, operations for <a href="CHAP004.htm#I2">4.2</a> <dt>Schunck classes and formations <a href="CHAP004.htm">4.0</a> <dt>SchunckClass <a href="CHAP004.htm#SSEC001.1">4.1.1</a> <dt>Set theoretical classes <a href="CHAP002.htm">2.0</a> <dt>set, of all primes <a href="CHAP006.htm#SSEC003.1">6.3.1</a> <dt>SetIsFittingClass <a href="CHAP003.htm#SSEC003.3">3.3.3</a> <dt>SetIsFittingFormation <a href="CHAP003.htm#SSEC003.12">3.3.12</a> <dt>SetIsFormation <a href="CHAP003.htm#I7">3.3</a> <dt>SetIsOrdinaryFormation <a href="CHAP003.htm#SSEC003.6">3.3.6</a> <dt>SetIsSaturatedFittingFormation <a href="CHAP003.htm#SSEC003.15">3.3.15</a> <dt>SetIsSaturatedFormation <a href="CHAP003.htm#SSEC003.9">3.3.9</a> <dt>Socle <a href="CHAP005.htm#SSEC005.1">5.5.1</a> <dt>SocleComplement <a href="CHAP004.htm#SSEC003.2">4.3.2</a> <dt>SocleComponents <a href="CHAP005.htm#SSEC005.3">5.5.3</a> <dt>SolvableSocle <a href="CHAP005.htm#SSEC005.2">5.5.2</a> <dt>SolvableSocleComponents <a href="CHAP005.htm#SSEC005.4">5.5.4</a> <dt>supersolvable groups, class of <a href="CHAP006.htm#I4">6.1</a> <dt>SupersolvableProjector <a href="CHAP006.htm#SSEC002.2">6.2.2</a> </dl><p> <H2><A NAME="idxT">T</A></H2> <dl> <dt>trivial groups, class of <a href="CHAP006.htm#I0">6.1</a> </dl><p> <H2><A NAME="idxU">U</A></H2> <dl> <dt>Union <a href="CHAP002.htm#SSEC003.3">2.3.3</a> </dl><p> <H2><A NAME="idxV">V</A></H2> <dl> <dt>View, for classes <a href="CHAP002.htm#SSEC001.3">2.1.3</a> </dl><p> [<a href="chapters.htm">Up</a>]<p> <P> <address>CRISP manual<br>June 2007 </address></body></html>
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