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<html><head><title>automgrp : a GAP 4 package - Index </title></head>
<body text="#000000" bgcolor="#ffffff"> <h1><font face="Gill Sans,Helvetica,Arial">automgrp</font> : a <font face="Gill Sans,Helveti <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> <a href="#idxW">W</A> <H2><A NAME="idxA">A</A></H2> <dl> <dt>AbelImage <a href="CHAP002.htm#SSEC003.24">2.3.24</a> <dt>action, of tree homomorphism on letter <a href="CHAP003.htm#SSEC003.2">3.3.2</a> <dt>action, of tree homomorphism on vertex <a href="CHAP003.htm#SSEC003.2">3.3.2</a> <dt>AddingMachine <a href="CHAP005.htm#SSEC003.5">5.3.5</a> <dt>AdjacencyMatrix <a href="CHAP004.htm#SSEC002.8">4.2.8</a> <dt>AG_AddRelators <a href="CHAP002.htm#SSEC006.2">2.6.2</a> <dt>AG_RewritingSystemRules <a href="CHAP002.htm#SSEC006.4">2.6.4</a> <dt>AG_UpdateRewritingSystem <a href="CHAP002.htm#SSEC006.3">2.6.3</a> <dt>AG_UseRewritingSystem <a href="CHAP002.htm#SSEC006.1">2.6.1</a> <dt>Airplane <a href="CHAP005.htm#SSEC003.17">5.3.17</a> <dt>AleshinGroup <a href="CHAP005.htm#SSEC003.7">5.3.7</a> <dt>AllSections <a href="CHAP003.htm#SSEC004.2">3.4.2</a> <dt>AreEquivalentAutomata <a href="CHAP004.htm#SSEC002.22">4.2.22</a> <dt>AutomatonGroup <a href="CHAP002.htm#SSEC001.1">2.1.1</a> <dt>AutomatonList, for automaton <a href="CHAP004.htm#SSEC001.5">4.1.5</a> <dt>AutomatonList, for tree homomorphism (semi)group <a href="CHAP002.htm#SSEC002.17">2.2. <dt>AutomatonNucleus <a href="CHAP004.htm#SSEC002.21">4.2.21</a> <dt>AutomatonSemigroup <a href="CHAP002.htm#SSEC001.2">2.1.2</a> <dt>AutomGrp2FR <a href="CHAP005.htm#SSEC001.2">5.1.2</a> <dt>AutomPortrait <a href="CHAP003.htm#SSEC005.1">3.5.1</a> <dt>AutomPortraitBoundary <a href="CHAP003.htm#SSEC005.1">3.5.1</a> <dt>AutomPortraitDepth <a href="CHAP003.htm#SSEC005.1">3.5.1</a> </dl><p> <H2><A NAME="idxB">B</A></H2> <dl> <dt>BartholdiGrigorchukGroup <a href="CHAP005.htm#SSEC003.13">5.3.13</a> <dt>BartholdiNonunifExponGroup <a href="CHAP005.htm#SSEC003.15">5.3.15</a> <dt>Basic properties of groups and semigroups <a href="CHAP002.htm#SECT002">2.2</a> <dt>Basilica <a href="CHAP005.htm#SSEC003.3">5.3.3</a> <dt>Bellaterra <a href="CHAP005.htm#SSEC003.8">5.3.8</a> </dl><p> <H2><A NAME="idxC">C</A></H2> <dl> <dt>ContainsSphericallyTransitiveElement <a href="CHAP002.htm#SSEC002.6">2.2.6</a> <dt>Contracting groups <a href="CHAP002.htm#SECT005">2.5</a> <dt>ContractingLevel <a href="CHAP002.htm#SSEC005.4">2.5.4</a> <dt>ContractingTable <a href="CHAP002.htm#SSEC005.5">2.5.5</a> <dt>Converters to and from FR package <a href="CHAP005.htm#SECT001">5.1</a> <dt>Creation of groups and semigroups <a href="CHAP002.htm#SECT001">2.1</a> <dt>Creation of tree automorphisms and homomorphisms <a href="CHAP003.htm#SECT001">3.1</a> </dl><p> <H2><A NAME="idxD">D</A></H2> <dl> <dt>Decompose <a href="CHAP003.htm#SSEC003.5">3.3.5</a> <dt>Definition <a href="CHAP004.htm#SECT001">4.1</a> <dt>DegreeOfTree <a href="CHAP002.htm#SSEC002.2">2.2.2</a> <dt>DiagonalPower <a href="CHAP002.htm#SSEC003.25">2.3.25</a> <dt>DisjointUnion <a href="CHAP004.htm#SSEC002.18">4.2.18</a> <dt>DoNotUseContraction <a href="CHAP002.htm#SSEC005.6">2.5.6</a> <dt>DualAutomaton <a href="CHAP004.htm#SSEC002.10">4.2.10</a> </dl><p> <H2><A NAME="idxE">E</A></H2> <dl> <dt>Elements of contracting groups <a href="CHAP003.htm#SECT005">3.5</a> <dt>Elements of groups and semigroups defined by wreath recursion <a href="CHAP003.htm#SECT00 </dl><p> <H2><A NAME="idxF">F</A></H2> <dl> <dt>FindElement <a href="CHAP002.htm#SSEC003.13">2.3.13</a> <dt>FindElementOfInfiniteOrder <a href="CHAP002.htm#SSEC003.14">2.3.14</a> <dt>FindElements <a href="CHAP002.htm#SSEC003.13">2.3.13</a> <dt>FindElementsOfInfiniteOrder <a href="CHAP002.htm#SSEC003.14">2.3.14</a> <dt>FindGroupRelations <a href="CHAP002.htm#SSEC003.10">2.3.10</a> <dt>FindNucleus <a href="CHAP002.htm#SSEC003.18">2.3.18</a> <dt>FindSemigroupRelations <a href="CHAP002.htm#SSEC003.11">2.3.11</a> <dt>FixesLevel <a href="CHAP002.htm#SSEC003.6">2.3.6</a> <dt>FixesVertex <a href="CHAP002.htm#SSEC003.7">2.3.7</a> <dt>FR2AutomGrp <a href="CHAP005.htm#SSEC001.1">5.1.1</a> </dl><p> <H2><A NAME="idxG">G</A></H2> <dl> <dt>GeneratingSetWithNucleus <a href="CHAP002.htm#SSEC005.2">2.5.2</a> <dt>GeneratingSetWithNucleusAutom <a href="CHAP002.htm#SSEC005.3">2.5.3</a> <dt>GrigorchukErschlerGroup <a href="CHAP005.htm#SSEC003.14">5.3.14</a> <dt>GrigorchukGroup <a href="CHAP005.htm#SSEC003.1">5.3.1</a> <dt>GroupNucleus <a href="CHAP002.htm#SSEC005.1">2.5.1</a> <dt>Growth <a href="CHAP002.htm#SSEC003.16">2.3.16</a> <dt>GuptaFabrikowskiGroup <a href="CHAP005.htm#SSEC003.12">5.3.12</a> <dt>GuptaSidki3Group <a href="CHAP005.htm#SSEC003.11">5.3.11</a> </dl><p> <H2><A NAME="idxH">H</A></H2> <dl> <dt>Hanoi3 <a href="CHAP005.htm#SSEC003.10">5.3.10</a> <dt>Hanoi4 <a href="CHAP005.htm#SSEC003.10">5.3.10</a> </dl><p> <H2><A NAME="idxI">I</A></H2> <dl> <dt>IMG_z2plusI <a href="CHAP005.htm#SSEC003.16">5.3.16</a> <dt>in <a href="CHAP003.htm#SSEC003.6">3.3.6</a> <dt>InfiniteDihedral <a href="CHAP005.htm#SSEC003.6">5.3.6</a> <dt>Installation instructions <a href="CHAP001.htm#SECT002">1.2</a> <dt>Introduction <a href="CHAP001.htm">1.0</a> <dt>InverseAutomaton <a href="CHAP004.htm#SSEC002.11">4.2.11</a> <dt>IsAcyclic <a href="CHAP004.htm#SSEC002.9">4.2.9</a> <dt>IsAmenable <a href="CHAP002.htm#SSEC002.15">2.2.15</a> <dt>IsAutomatonGroup <a href="CHAP002.htm#SSEC001.7">2.1.7</a> <dt>IsAutomGroup <a href="CHAP002.htm#SSEC001.6">2.1.6</a> <dt>IsBireversible <a href="CHAP004.htm#SSEC002.12">4.2.12</a> <dt>IsBounded <a href="CHAP004.htm#SSEC002.6">4.2.6</a> <dt>IsContracting <a href="CHAP002.htm#SSEC002.9">2.2.9</a> <dt>IsFiniteState, for tree homomorphism <a href="CHAP003.htm#SSEC004.1">3.4.1</a> <dt>IsFiniteState, for tree homomorphism (semi)group <a href="CHAP002.htm#SSEC004.1">2.4.1< <dt>IsFractal <a href="CHAP002.htm#SSEC002.3">2.2.3</a> <dt>IsFractalByWords <a href="CHAP002.htm#SSEC002.4">2.2.4</a> <dt>IsGeneratedByAutomatonOfPolynomialGrowth <a href="CHAP002.htm#SSEC002.11">2.2.11</a> <dt>IsGeneratedByBoundedAutomaton <a href="CHAP002.htm#SSEC002.12">2.2.12</a> <dt>IsInvertible <a href="CHAP004.htm#SSEC002.2">4.2.2</a> <dt>IsIRAutomaton <a href="CHAP004.htm#SSEC002.14">4.2.14</a> <dt>IsMDReduced <a href="CHAP004.htm#SSEC002.17">4.2.17</a> <dt>IsMDTrivial <a href="CHAP004.htm#SSEC002.16">4.2.16</a> <dt>IsMealyAutomaton <a href="CHAP004.htm#SSEC001.2">4.1.2</a> <dt>IsNoncontracting <a href="CHAP002.htm#SSEC002.10">2.2.10</a> <dt>IsOfPolynomialGrowth <a href="CHAP004.htm#SSEC002.5">4.2.5</a> <dt>IsOfSubexponentialGrowth <a href="CHAP002.htm#SSEC002.14">2.2.14</a> <dt>IsomorphicAutomGroup <a href="CHAP002.htm#SSEC004.2">2.4.2</a> <dt>IsomorphicAutomSemigroup <a href="CHAP002.htm#SSEC004.3">2.4.3</a> <dt>IsomorphismPermGroup <a href="CHAP002.htm#SSEC003.20">2.3.20</a> <dt>IsOne <a href="CHAP003.htm#SSEC002.3">3.2.3</a> <dt>IsOneContr <a href="CHAP003.htm#SSEC002.4">3.2.4</a> <dt>IsReversible <a href="CHAP004.htm#SSEC002.13">4.2.13</a> <dt>IsSelfSimGroup <a href="CHAP002.htm#SSEC001.8">2.1.8</a> <dt>IsSelfSimilar <a href="CHAP002.htm#SSEC002.8">2.2.8</a> <dt>IsSelfSimilarGroup <a href="CHAP002.htm#SSEC001.9">2.1.9</a> <dt>IsSphericallyTransitive, for tree homomorphism <a href="CHAP003.htm#SSEC002.1">3.2.1</ <dt>IsSphericallyTransitive, for tree homomorphism (semi)group <a href="CHAP002.htm#SSEC0 <dt>IsTransitiveOnLevel, for tree homomorphism <a href="CHAP003.htm#SSEC002.2">3.2.2</a> <dt>IsTransitiveOnLevel, for tree homomorphism (semi)group <a href="CHAP002.htm#SSEC002.7 <dt>IsTreeAutomorphismGroup <a href="CHAP002.htm#SSEC001.5">2.1.5</a> <dt>IsTrivial <a href="CHAP004.htm#SSEC002.1">4.2.1</a> <dt>Iterator <a href="CHAP002.htm#SSEC003.12">2.3.12</a> </dl><p> <H2><A NAME="idxL">L</A></H2> <dl> <dt>Lamplighter <a href="CHAP005.htm#SSEC003.4">5.3.4</a> <dt>LevelOfFaithfulAction <a href="CHAP002.htm#SSEC003.19">2.3.19</a> <dt>ListOfElements <a href="CHAP002.htm#SSEC003.17">2.3.17</a> </dl><p> <H2><A NAME="idxM">M</A></H2> <dl> <dt>MarkovOperator <a href="CHAP002.htm#SSEC003.22">2.3.22</a> <dt>MDReduction <a href="CHAP004.htm#SSEC002.15">4.2.15</a> <dt>MealyAutomaton <a href="CHAP004.htm#SSEC001.1">4.1.1</a> <dt>MihailovaSystem <a href="CHAP002.htm#SSEC003.23">2.3.23</a> <dt>MinimizationOfAutomaton <a href="CHAP004.htm#SSEC002.3">4.2.3</a> <dt>MinimizationOfAutomatonTrack <a href="CHAP004.htm#SSEC002.4">4.2.4</a> <dt>Miscellaneous <a href="CHAP005.htm">5.0</a> <dt>MonomorphismToAutomatonGroup <a href="CHAP002.htm#SSEC004.6">2.4.6</a> <dt>MonomorphismToAutomatonSemigroup <a href="CHAP002.htm#SSEC004.7">2.4.7</a> <dt>MultAutomAlphabet <a href="CHAP002.htm#SSEC003.26">2.3.26</a> </dl><p> <H2><A NAME="idxN">N</A></H2> <dl> <dt>Noninitial automata <a href="CHAP004.htm">4.0</a> <dt>NumberOfStates <a href="CHAP004.htm#SSEC001.3">4.1.3</a> <dt>NumberOfVertex <a href="CHAP005.htm#SSEC002.1">5.2.1</a> </dl><p> <H2><A NAME="idxO">O</A></H2> <dl> <dt>Operations with groups and semigroups <a href="CHAP002.htm#SECT003">2.3</a> <dt>Operations with tree automorphisms and homomorphisms <a href="CHAP003.htm#SECT003">3.3</ <dt>OrbitOfVertex <a href="CHAP003.htm#SSEC003.7">3.3.7</a> <dt>Order <a href="CHAP003.htm#SSEC002.5">3.2.5</a> <dt>OrderUsingSections <a href="CHAP003.htm#SSEC002.6">3.2.6</a> </dl><p> <H2><A NAME="idxP">P</A></H2> <dl> <dt>Perm <a href="CHAP003.htm#SSEC002.7">3.2.7</a> <dt>PermActionOnLevel <a href="CHAP003.htm#SSEC003.9">3.3.9</a> <dt>PermGroupOnLevel <a href="CHAP002.htm#SSEC003.1">2.3.1</a> <dt>PermOnLevel <a href="CHAP003.htm#SSEC002.8">3.2.8</a> <dt>PermOnLevelAsMatrix <a href="CHAP003.htm#SSEC002.9">3.2.9</a> <dt>PolynomialDegreeOfGrowth <a href="CHAP004.htm#SSEC002.7">4.2.7</a> <dt>PolynomialDegreeOfGrowthOfUnderlyingAutomaton <a href="CHAP002.htm#SSEC002.13">2.2 <dt>PrintOrbitOfVertex <a href="CHAP003.htm#SSEC003.8">3.3.8</a> <dt>product, for noninitial automata <a href="CHAP004.htm#SSEC002.19">4.2.19</a> <dt>product, for tree homomorphisms <a href="CHAP003.htm#SSEC003.1">3.3.1</a> <dt>Projection <a href="CHAP002.htm#SSEC003.8">2.3.8</a> <dt>ProjectionNC <a href="CHAP002.htm#SSEC003.8">2.3.8</a> <dt>ProjStab <a href="CHAP002.htm#SSEC003.9">2.3.9</a> <dt>Properties and attributes of tree automorphisms and homomorphisms <a href="CHAP003.htm#S <dt>Properties and operations with group and semigroup elements <a href="CHAP003.htm">3.0</a> <dt>Properties and operations with groups and semigroups <a href="CHAP002.htm">2.0</a> </dl><p> <H2><A NAME="idxQ">Q</A></H2> <dl> <dt>Quick example <a href="CHAP001.htm#SECT003">1.3</a> </dl><p> <H2><A NAME="idxR">R</A></H2> <dl> <dt>Rabbit <a href="CHAP005.htm#SSEC003.17">5.3.17</a> <dt>Random <a href="CHAP002.htm#SSEC003.21">2.3.21</a> <dt>RecurList, for tree homomorphism (semi)group <a href="CHAP002.htm#SSEC002.18">2.2.18</a> <dt>Representative <a href="CHAP003.htm#SSEC001.3">3.1.3</a> <dt>Rewriting Systems <a href="CHAP002.htm#SECT006">2.6</a> </dl><p> <H2><A NAME="idxS">S</A></H2> <dl> <dt>Section, for tree homomorphism <a href="CHAP003.htm#SSEC003.3">3.3.3</a> <dt>Sections <a href="CHAP003.htm#SSEC003.4">3.3.4</a> <dt>Self-similar groups and semigroups defined by the wreath recursion <a href="CHAP002.htm#S <dt>SelfSimilarGroup <a href="CHAP002.htm#SSEC001.3">2.1.3</a> <dt>SelfSimilarSemigroup <a href="CHAP002.htm#SSEC001.4">2.1.4</a> <dt>Short math background <a href="CHAP001.htm#SECT001">1.1</a> <dt>SizeOfAlphabet <a href="CHAP004.htm#SSEC001.4">4.1.4</a> <dt>Some predefined groups <a href="CHAP005.htm#SECT003">5.3</a> <dt>SphericallyTransitiveElement <a href="CHAP002.htm#SSEC003.15">2.3.15</a> <dt>StabilizerOfFirstLevel <a href="CHAP002.htm#SSEC003.4">2.3.4</a> <dt>StabilizerOfLevel <a href="CHAP002.htm#SSEC003.3">2.3.3</a> <dt>StabilizerOfVertex <a href="CHAP002.htm#SSEC003.5">2.3.5</a> <dt>SubautomatonWithStates <a href="CHAP004.htm#SSEC002.20">4.2.20</a> <dt>SushchanskyGroup <a href="CHAP005.htm#SSEC003.9">5.3.9</a> </dl><p> <H2><A NAME="idxT">T</A></H2> <dl> <dt>Tools <a href="CHAP004.htm#SECT002">4.2</a> <dt>TopDegreeOfTree <a href="CHAP002.htm#SSEC002.1">2.2.1</a> <dt>TransformationOnFirstLevel <a href="CHAP003.htm#SSEC002.10">3.2.10</a> <dt>TransformationOnLevel <a href="CHAP003.htm#SSEC002.10">3.2.10</a> <dt>TransformationOnLevelAsMatrix <a href="CHAP003.htm#SSEC002.11">3.2.11</a> <dt>TransformationSemigroupOnLevel <a href="CHAP002.htm#SSEC003.2">2.3.2</a> <dt>TreeAutomorphism <a href="CHAP003.htm#SSEC001.1">3.1.1</a> <dt>TreeHomomorphism <a href="CHAP003.htm#SSEC001.2">3.1.2</a> <dt>Trees <a href="CHAP005.htm#SECT002">5.2</a> <dt>TwoStateSemigroupOfIntermediateGrowth <a href="CHAP005.htm#SSEC003.18">5.3.18</a> </dl><p> <H2><A NAME="idxU">U</A></H2> <dl> <dt>UnderlyingAutomaton <a href="CHAP002.htm#SSEC002.16">2.2.16</a> <dt>UnderlyingAutomatonGroup <a href="CHAP002.htm#SSEC004.4">2.4.4</a> <dt>UnderlyingAutomatonSemigroup <a href="CHAP002.htm#SSEC004.5">2.4.5</a> <dt>UnderlyingAutomFamily <a href="CHAP002.htm#SSEC003.27">2.3.27</a> <dt>UniversalD_omega <a href="CHAP005.htm#SSEC003.19">5.3.19</a> <dt>UniversalGrigorchukGroup <a href="CHAP005.htm#SSEC003.2">5.3.2</a> <dt>UseContraction <a href="CHAP002.htm#SSEC005.6">2.5.6</a> </dl><p> <H2><A NAME="idxV">V</A></H2> <dl> <dt>VertexNumber <a href="CHAP005.htm#SSEC002.2">5.2.2</a> </dl><p> <H2><A NAME="idxW">W</A></H2> <dl> <dt>Word <a href="CHAP003.htm#SSEC002.12">3.2.12</a> </dl><p> [<a href="chapters.htm">Up</a>]<p> <P> <address>automgrp manual<br>January 2025 </address></body></html> ¤ Dauer der Verarbeitung: 0.14 Sekunden (vorverarbeitet) ¤*© Formatika GbR, 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