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<html><head><title>SONATA : a GAP 4 package - Index </title></head> <body text="#000000" bgcolor="#ffffff"> <h1><font face="Gill Sans,Helvetica,Arial">SONATA</font> : a <font face="Gill Sans,Helvetica <p> <a href="#idx_">_</A> <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="#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="#idxW">W</A> <a href="#idxZ">Z</A> <H2><A NAME="idx_">_</A></H2> <dl> <dt>/ <a href="CHAP006.htm#SSEC014.2">6.14.2</a> <dt>= <a href="CHAP006.htm#SSEC010.1">6.10.1</a> </dl><p> <H2><A NAME="idxA">A</A></H2> <dl> <dt>Accessing nearring elements <a href="CHAP002.htm#SECT006">2.6</a> <dt>Accessing the information about a nearring stored in the library <a href="CHAP003.htm#SECT <dt>ActionOfNearRingOnNGroup <a href="CHAP008.htm#SSEC003.3">8.3.3</a> <dt>AllExceptionalNearFields <a href="CHAP010.htm#SSEC003.2">10.3.2</a> <dt>AllLibraryNearRings <a href="CHAP003.htm#SSEC001.3">3.1.3</a> <dt>AllLibraryNearRingsWithOne <a href="CHAP003.htm#SSEC001.6">3.1.6</a> <dt>Arbitrary functions on groups: EndoMappings <a href="CHAP004.htm">4.0</a> <dt>AsEndoMapping <a href="CHAP004.htm#SSEC001.3">4.1.3</a> <dt>AsExplicitMultiplicationNearRing <a href="CHAP005.htm#SSEC004.2">5.4.2</a> <dt>AsGroupGeneralMappingByImages <a href="CHAP004.htm#SSEC001.4">4.1.4</a> <dt>AsGroupReductElement <a href="CHAP002.htm#SSEC006.2">2.6.2</a> <dt>AsList, near ring ideals <a href="CHAP006.htm#SSEC005.1">6.5.1</a> <dt>AsList, near rings <a href="CHAP002.htm#SSEC007.1">2.7.1</a> <dt>AsNearRingElement <a href="CHAP002.htm#SSEC006.1">2.6.1</a> <dt>AsPermGroup <a href="CHAP001.htm#SSEC012.1">1.12.1</a> <dt>AsSortedList, near ring ideals <a href="CHAP006.htm#SSEC005.2">6.5.2</a> <dt>AsSortedList, near rings <a href="CHAP002.htm#SSEC007.2">2.7.2</a> <dt>AsTransformationNearRing <a href="CHAP005.htm#SSEC004.1">5.4.1</a> <dt>AutomorphismNearRing <a href="CHAP005.htm#SSEC002.6">5.2.6</a> <dt>Automorphisms <a href="CHAP001.htm#SSEC004.1">1.4.1</a> <dt>Automorphisms, near rings <a href="CHAP002.htm#SSEC013.1">2.13.1</a> </dl><p> <H2><A NAME="idxB">B</A></H2> <dl> <dt>BlockIntersectionNumbers <a href="CHAP011.htm#SSEC002.6">11.2.6</a> <dt>BlockIntersectionNumbersK <a href="CHAP011.htm#SSEC002.6">11.2.6</a> <dt>BlocksIncidentPoints <a href="CHAP011.htm#SSEC003.3">11.3.3</a> <dt>BlocksOfDesign <a href="CHAP011.htm#SSEC002.2">11.2.2</a> </dl><p> <H2><A NAME="idxC">C</A></H2> <dl> <dt>CentralizerNearRing <a href="CHAP005.htm#SSEC002.12">5.2.12</a> <dt>ClosureNearRingIdeal <a href="CHAP006.htm#SSEC011.5">6.11.5</a> <dt>ClosureNearRingLeftIdeal <a href="CHAP006.htm#SSEC011.3">6.11.3</a> <dt>ClosureNearRingRightIdeal <a href="CHAP006.htm#SSEC011.4">6.11.4</a> <dt>Commutators <a href="CHAP006.htm#SECT012">6.12</a> <dt>Comparision of ideals <a href="CHAP006.htm#SECT010">6.10</a> <dt>CompatibleFunctionNearRing <a href="CHAP005.htm#SSEC002.8">5.2.8</a> <dt>CongruenceNoetherianQuotient, for nearrings of polynomial functions <a href="CHAP005.h <dt>CongruenceNoetherianQuotientForInnerAutomorphismNearRings , for inner automorphism <dt>ConstantEndoMapping <a href="CHAP004.htm#SSEC001.7">4.1.7</a> <dt>Constructing a design <a href="CHAP011.htm#SECT001">11.1</a> <dt>Constructing subnearrings <a href="CHAP002.htm#SECT017">2.17</a> <dt>Constructing transformation nearrings <a href="CHAP005.htm#SECT001">5.1</a> <dt>Construction of N-groups <a href="CHAP008.htm#SECT001">8.1</a> <dt>Construction of nearring ideals <a href="CHAP006.htm#SECT001">6.1</a> <dt>Construction of nearrings <a href="CHAP002.htm#SECT002">2.2</a> <dt>Coset representatives <a href="CHAP001.htm#SECT010">1.10</a> </dl><p> <H2><A NAME="idxD">D</A></H2> <dl> <dt>Defining a nearring multiplication <a href="CHAP002.htm#SECT001">2.1</a> <dt>Defining endo mappings <a href="CHAP004.htm#SECT001">4.1</a> <dt>DegreeOfIrredFpfRep2 <a href="CHAP009.htm#SSEC002.4">9.2.4</a> <dt>DegreeOfIrredFpfRep3 <a href="CHAP009.htm#SSEC002.5">9.2.5</a> <dt>DegreeOfIrredFpfRep4 <a href="CHAP009.htm#SSEC002.6">9.2.6</a> <dt>DegreeOfIrredFpfRepCyclic <a href="CHAP009.htm#SSEC002.2">9.2.2</a> <dt>DegreeOfIrredFpfRepMetacyclic <a href="CHAP009.htm#SSEC002.3">9.2.3</a> <dt>DesignFromFerreroPair <a href="CHAP011.htm#SSEC001.4">11.1.4</a> <dt>DesignFromIncidenceMat <a href="CHAP011.htm#SSEC001.2">11.1.2</a> <dt>DesignFromPlanarNearRing <a href="CHAP011.htm#SSEC001.3">11.1.3</a> <dt>DesignFromPointsAndBlocks <a href="CHAP011.htm#SSEC001.1">11.1.1</a> <dt>DesignFromWdNearRing <a href="CHAP011.htm#SSEC001.5">11.1.5</a> <dt>DesignParameter <a href="CHAP011.htm#SSEC002.3">11.2.3</a> <dt>Designs <a href="CHAP011.htm">11.0</a> <dt>Dickson nearfields <a href="CHAP010.htm#SECT002">10.2</a> <dt>Dickson numbers <a href="CHAP010.htm#SECT001">10.1</a> <dt>DicksonNearFields <a href="CHAP010.htm#SSEC002.1">10.2.1</a> <dt>Direct products of nearrings <a href="CHAP002.htm#SECT003">2.3</a> <dt>DirectProductNearRing <a href="CHAP002.htm#SSEC003.1">2.3.1</a> <dt>DistributiveElements <a href="CHAP002.htm#SSEC021.2">2.21.2</a> <dt>Distributivity in a nearring <a href="CHAP002.htm#SECT021">2.21</a> <dt>Distributors <a href="CHAP002.htm#SSEC021.1">2.21.1</a> </dl><p> <H2><A NAME="idxE">E</A></H2> <dl> <dt>Elements of a nearring with special properties <a href="CHAP002.htm#SECT022">2.22</a> <dt>EndoMappingByFunction <a href="CHAP004.htm#SSEC001.2">4.1.2</a> <dt>EndoMappingByPositionList <a href="CHAP004.htm#SSEC001.1">4.1.1</a> <dt>EndomorphismNearRing <a href="CHAP005.htm#SSEC002.5">5.2.5</a> <dt>Endomorphisms <a href="CHAP001.htm#SSEC003.1">1.3.1</a> <dt>Endomorphisms, near rings <a href="CHAP002.htm#SSEC012.1">2.12.1</a> <dt>Enumerator, near ring ideals <a href="CHAP006.htm#SSEC005.3">6.5.3</a> <dt>Enumerator, near rings <a href="CHAP002.htm#SSEC007.3">2.7.3</a> <dt>Exceptional nearfields <a href="CHAP010.htm#SECT003">10.3</a> <dt>ExceptionalNearFields <a href="CHAP010.htm#SSEC003.1">10.3.1</a> <dt>ExplicitMultiplicationNearRing <a href="CHAP002.htm#SSEC002.1">2.2.1</a> <dt>ExplicitMultiplicationNearRingNC <a href="CHAP002.htm#SSEC002.2">2.2.2</a> <dt>Extracting nearrings from the library <a href="CHAP003.htm#SECT001">3.1</a> </dl><p> <H2><A NAME="idxF">F</A></H2> <dl> <dt>Factor nearrings <a href="CHAP006.htm#SECT014">6.14</a> <dt>FactorNearRing <a href="CHAP006.htm#SSEC014.1">6.14.1</a> <dt>Fixed-point-free automorphism groups <a href="CHAP009.htm">9.0</a> <a href="CHAP009.htm#S <dt>Fixed-point-free automorphism groups and Frobenius groups <a href="CHAP009.htm#SECT001 <dt>Fixed-point-free representations <a href="CHAP009.htm#SECT002">9.2</a> <dt>FpfAutomorphismGroups2 <a href="CHAP009.htm#SSEC003.3">9.3.3</a> <dt>FpfAutomorphismGroups3 <a href="CHAP009.htm#SSEC003.4">9.3.4</a> <dt>FpfAutomorphismGroups4 <a href="CHAP009.htm#SSEC003.5">9.3.5</a> <dt>FpfAutomorphismGroupsCyclic <a href="CHAP009.htm#SSEC003.1">9.3.1</a> <dt>FpfAutomorphismGroupsMaxSize <a href="CHAP009.htm#SSEC001.2">9.1.2</a> <dt>FpfAutomorphismGroupsMetacyclic <a href="CHAP009.htm#SSEC003.2">9.3.2</a> <dt>FpfRepresentations2 <a href="CHAP009.htm#SSEC002.9">9.2.9</a> <dt>FpfRepresentations3 <a href="CHAP009.htm#SSEC002.10">9.2.10</a> <dt>FpfRepresentations4 <a href="CHAP009.htm#SSEC002.11">9.2.11</a> <dt>FpfRepresentationsCyclic <a href="CHAP009.htm#SSEC002.7">9.2.7</a> <dt>FpfRepresentationsMetacyclic <a href="CHAP009.htm#SSEC002.8">9.2.8</a> <dt>FrobeniusGroup <a href="CHAP009.htm#SSEC001.3">9.1.3</a> <dt>Functions for N-groups <a href="CHAP008.htm#SECT003">8.3</a> </dl><p> <H2><A NAME="idxG">G</A></H2> <dl> <dt>Gamma <a href="CHAP005.htm#SSEC003.1">5.3.1</a> <dt>Generators of nearring ideals <a href="CHAP006.htm#SECT004">6.4</a> <dt>GeneratorsOfNearRing <a href="CHAP002.htm#SSEC009.1">2.9.1</a> <dt>GeneratorsOfNearRingIdeal <a href="CHAP006.htm#SSEC004.1">6.4.1</a> <dt>GeneratorsOfNearRingLeftIdeal <a href="CHAP006.htm#SSEC004.2">6.4.2</a> <dt>GeneratorsOfNearRingRightIdeal <a href="CHAP006.htm#SSEC004.3">6.4.3</a> <dt>Graphic ideal lattices (XGAP only) <a href="CHAP007.htm">7.0</a> <dt>GraphicIdealLattice <a href="CHAP007.htm#">7.0</a> <dt>GraphOfMapping <a href="CHAP004.htm#SSEC004.1">4.4.1</a> <dt>Group automorphisms <a href="CHAP001.htm#SECT004">1.4</a> <dt>Group endomorphisms <a href="CHAP001.htm#SECT003">1.3</a> <dt>Group reducts of ideals <a href="CHAP006.htm#SECT009">6.9</a> <dt>GroupReduct <a href="CHAP002.htm#SSEC011.1">2.11.1</a> <dt>GroupReduct, near ring ideals <a href="CHAP006.htm#SSEC009.1">6.9.1</a> </dl><p> <H2><A NAME="idxI">I</A></H2> <dl> <dt>Ideals of N-groups <a href="CHAP008.htm#SECT006">8.6</a> <dt>IdempotentElements <a href="CHAP002.htm#SSEC022.2">2.22.2</a> <dt>Identifying nearrings <a href="CHAP003.htm#SECT002">3.2</a> <dt>Identity <a href="CHAP002.htm#SSEC019.1">2.19.1</a> <dt>Identity of a nearring <a href="CHAP002.htm#SECT019">2.19</a> <dt>IdentityEndoMapping <a href="CHAP004.htm#SSEC001.6">4.1.6</a> <dt>IdLibraryNearRing <a href="CHAP003.htm#SSEC002.1">3.2.1</a> <dt>IdLibraryNearRingWithOne <a href="CHAP003.htm#SSEC002.2">3.2.2</a> <dt>IdTWGroup <a href="CHAP001.htm#SSEC001.2">1.1.2</a> <dt>in <a href="CHAP006.htm#SSEC007.1">6.7.1</a> <dt>IncidenceMat <a href="CHAP011.htm#SSEC002.4">11.2.4</a> <dt>Inner automorphisms of a group <a href="CHAP001.htm#SECT005">1.5</a> <dt>InnerAutomorphismNearRing <a href="CHAP005.htm#SSEC002.7">5.2.7</a> <dt>InnerAutomorphisms <a href="CHAP001.htm#SSEC005.1">1.5.1</a> <dt>Intersection <a href="CHAP006.htm#SSEC011.2">6.11.2</a> <dt>Intersection of nearrings <a href="CHAP002.htm#SECT018">2.18</a> <dt>Intersection, for nearring ideals <a href="CHAP006.htm#SSEC011.1">6.11.1</a> <dt>Intersection, for nearrings <a href="CHAP002.htm#SSEC018.1">2.18.1</a> <dt>Invariant subgroups <a href="CHAP001.htm#SECT009">1.9</a> <dt>Invariant subnearrings <a href="CHAP002.htm#SECT016">2.16</a> <dt>InvariantSubNearRings <a href="CHAP002.htm#SSEC016.1">2.16.1</a> <dt>Is1AffineComplete <a href="CHAP005.htm#SSEC002.11">5.2.11</a> <dt>Is2TameNGroup <a href="CHAP008.htm#SSEC007.3">8.7.3</a> <dt>Is3TameNGroup <a href="CHAP008.htm#SSEC007.4">8.7.4</a> <dt>IsAbelianNearRing <a href="CHAP002.htm#SSEC023.1">2.23.1</a> <dt>IsAbstractAffineNearRing <a href="CHAP002.htm#SSEC023.2">2.23.2</a> <dt>IsBooleanNearRing <a href="CHAP002.htm#SSEC023.3">2.23.3</a> <dt>IsCharacteristicInParent <a href="CHAP001.htm#SSEC009.3">1.9.3</a> <dt>IsCharacteristicSubgroup <a href="CHAP001.htm#SSEC009.2">1.9.2</a> <dt>IsCircularDesign <a href="CHAP011.htm#SSEC002.7">11.2.7</a> <dt>IsCommutative <a href="CHAP002.htm#SSEC023.7">2.23.7</a> <dt>IsCompatible <a href="CHAP008.htm#SSEC007.1">8.7.1</a> <dt>IsCompatibleEndoMapping <a href="CHAP005.htm#SSEC002.10">5.2.10</a> <dt>IsConstantEndoMapping <a href="CHAP004.htm#SSEC002.2">4.2.2</a> <dt>IsDgNearRing <a href="CHAP002.htm#SSEC023.8">2.23.8</a> <dt>IsDistributiveEndoMapping <a href="CHAP004.htm#SSEC002.3">4.2.3</a> <dt>IsDistributiveNearRing <a href="CHAP002.htm#SSEC021.3">2.21.3</a> <dt>IsEndoMapping <a href="CHAP004.htm#SSEC001.5">4.1.5</a> <dt>IsExplicitMultiplicationNearRing <a href="CHAP002.htm#SSEC002.4">2.2.4</a> <dt>IsFpfAutomorphismGroup <a href="CHAP009.htm#SSEC001.1">9.1.1</a> <dt>IsFpfRepresentation <a href="CHAP009.htm#SSEC002.1">9.2.1</a> <dt>IsFullinvariant <a href="CHAP001.htm#SSEC009.4">1.9.4</a> <dt>IsFullinvariantInParent <a href="CHAP001.htm#SSEC009.5">1.9.5</a> <dt>IsFullTransformationNearRing <a href="CHAP005.htm#SSEC002.3">5.2.3</a> <dt>IsIdentityEndoMapping <a href="CHAP004.htm#SSEC002.1">4.2.1</a> <dt>IsIntegralNearRing <a href="CHAP002.htm#SSEC023.9">2.23.9</a> <dt>IsInvariantUnderMaps <a href="CHAP001.htm#SSEC009.1">1.9.1</a> <dt>IsIsomorphicGroup <a href="CHAP001.htm#SSEC006.1">1.6.1</a> <dt>IsIsomorphicNearRing <a href="CHAP002.htm#SSEC014.1">2.14.1</a> <dt>IsLibraryNearRing <a href="CHAP003.htm#SECT003">3.3</a> <a href="CHAP003.htm#SSEC003.1"> <dt>IsMaximalNearRingIdeal <a href="CHAP006.htm#SSEC003.2">6.3.2</a> <dt>IsMonogenic <a href="CHAP008.htm#SSEC007.5">8.7.5</a> <dt>IsN0SimpleNGroup <a href="CHAP008.htm#SSEC006.5">8.6.5</a> <dt>IsNearField <a href="CHAP002.htm#SSEC023.13">2.23.13</a> <dt>IsNearRing <a href="CHAP002.htm#SSEC002.3">2.2.3</a> <dt>IsNearRingIdeal <a href="CHAP006.htm#SSEC002.4">6.2.4</a> <dt>IsNearRingLeftIdeal <a href="CHAP006.htm#SSEC002.2">6.2.2</a> <dt>IsNearRingMultiplication <a href="CHAP002.htm#SSEC001.1">2.1.1</a> <dt>IsNearRingRightIdeal <a href="CHAP006.htm#SSEC002.3">6.2.3</a> <dt>IsNearRingUnit <a href="CHAP002.htm#SSEC020.1">2.20.1</a> <dt>IsNearRingWithOne <a href="CHAP002.htm#SSEC019.3">2.19.3</a> <dt>IsNGroup <a href="CHAP008.htm#SSEC003.1">8.3.1</a> <dt>IsNIdeal <a href="CHAP008.htm#SSEC006.3">8.6.3</a> <dt>IsNilNearRing <a href="CHAP002.htm#SSEC023.4">2.23.4</a> <dt>IsNilpotentFreeNearRing <a href="CHAP002.htm#SSEC023.6">2.23.6</a> <dt>IsNilpotentNearRing <a href="CHAP002.htm#SSEC023.5">2.23.5</a> <dt>IsNRI <a href="CHAP006.htm#SSEC002.1">6.2.1</a> <dt>IsNSubgroup <a href="CHAP008.htm#SSEC004.3">8.4.3</a> <dt>Isomorphic groups <a href="CHAP001.htm#SECT006">1.6</a> <dt>Isomorphic nearrings <a href="CHAP002.htm#SECT014">2.14</a> <dt>IsPairOfDicksonNumbers <a href="CHAP010.htm#SSEC001.1">10.1.1</a> <dt>IsPlanarNearRing <a href="CHAP002.htm#SSEC023.14">2.23.14</a> <dt>IsPointIncidentBlock <a href="CHAP011.htm#SSEC003.1">11.3.1</a> <dt>IsPrimeNearRing <a href="CHAP002.htm#SSEC023.10">2.23.10</a> <dt>IsPrimeNearRingIdeal <a href="CHAP006.htm#SSEC003.1">6.3.1</a> <dt>IsQuasiregularNearRing <a href="CHAP002.htm#SSEC023.11">2.23.11</a> <dt>IsRegularNearRing <a href="CHAP002.htm#SSEC023.12">2.23.12</a> <dt>IsSimpleNearRing <a href="CHAP006.htm#SSEC013.1">6.13.1</a> <dt>IsSimpleNGroup <a href="CHAP008.htm#SSEC006.4">8.6.4</a> <dt>IsStronglyMonogenic <a href="CHAP008.htm#SSEC007.6">8.7.6</a> <dt>IsSubgroupNearRingLeftIdeal <a href="CHAP006.htm#SSEC002.5">6.2.5</a> <dt>IsSubgroupNearRingRightIdeal <a href="CHAP006.htm#SSEC002.6">6.2.6</a> <dt>IsTameNGroup <a href="CHAP008.htm#SSEC007.2">8.7.2</a> <dt>IsWdNearRing <a href="CHAP002.htm#SSEC023.15">2.23.15</a> </dl><p> <H2><A NAME="idxL">L</A></H2> <dl> <dt>LibraryNearRing <a href="CHAP003.htm#SSEC001.1">3.1.1</a> <dt>LibraryNearRingInfo <a href="CHAP003.htm#SSEC004.1">3.4.1</a> <dt>LibraryNearRingWithOne <a href="CHAP003.htm#SSEC001.4">3.1.4</a> <dt>LocalInterpolationNearRing <a href="CHAP005.htm#SSEC002.14">5.2.14</a> </dl><p> <H2><A NAME="idxM">M</A></H2> <dl> <dt>MapNearRing <a href="CHAP005.htm#SSEC002.1">5.2.1</a> <dt>Membership of an ideal <a href="CHAP006.htm#SECT007">6.7</a> <dt>Modified symbols for the operation tables <a href="CHAP002.htm#SECT005">2.5</a> </dl><p> <H2><A NAME="idxN">N</A></H2> <dl> <dt>N-groups <a href="CHAP008.htm">8.0</a> <dt>N-subgroups <a href="CHAP008.htm#SECT004">8.4</a> <dt>N0-subgroups <a href="CHAP008.htm#SECT005">8.5</a> <dt>N0Subgroups <a href="CHAP008.htm#SSEC005.1">8.5.1</a> <dt>Near-ring ideal elements <a href="CHAP006.htm#SECT005">6.5</a> <dt>Nearfields, planar nearrings and weakly divisible nearrings <a href="CHAP010.htm">10.0</a> <dt>Nearring automorphisms <a href="CHAP002.htm#SECT013">2.13</a> <dt>Nearring elements <a href="CHAP002.htm#SECT007">2.7</a> <dt>Nearring endomorphisms <a href="CHAP002.htm#SECT012">2.12</a> <dt>Nearring generators <a href="CHAP002.htm#SECT009">2.9</a> <dt>Nearring ideals <a href="CHAP006.htm">6.0</a> <dt>Nearring radicals <a href="CHAP008.htm#SECT009">8.9</a> <dt>NearRingActingOnNGroup <a href="CHAP008.htm#SSEC003.2">8.3.2</a> <dt>NearRingCommutator <a href="CHAP006.htm#SSEC012.1">6.12.1</a> <dt>NearRingIdealByGenerators <a href="CHAP006.htm#SSEC001.1">6.1.1</a> <dt>NearRingIdealBySubgroupNC <a href="CHAP006.htm#SSEC001.4">6.1.4</a> <dt>NearRingIdeals <a href="CHAP006.htm#SSEC001.7">6.1.7</a> <dt>NearRingLeftIdealByGenerators <a href="CHAP006.htm#SSEC001.2">6.1.2</a> <dt>NearRingLeftIdealBySubgroupNC <a href="CHAP006.htm#SSEC001.5">6.1.5</a> <dt>NearRingLeftIdeals <a href="CHAP006.htm#SSEC001.8">6.1.8</a> <dt>NearRingMultiplicationByOperationTable <a href="CHAP002.htm#SSEC001.2">2.1.2</a> <dt>NearRingRightIdealByGenerators <a href="CHAP006.htm#SSEC001.3">6.1.3</a> <dt>NearRingRightIdealBySubgroupNC <a href="CHAP006.htm#SSEC001.6">6.1.6</a> <dt>NearRingRightIdeals <a href="CHAP006.htm#SSEC001.9">6.1.9</a> <dt>Nearrings <a href="CHAP002.htm">2.0</a> <dt>Nearrings of transformations <a href="CHAP005.htm#SECT002">5.2</a> <dt>NearRingUnits <a href="CHAP002.htm#SSEC020.2">2.20.2</a> <dt>NGroup <a href="CHAP008.htm#SSEC001.1">8.1.1</a> <dt>NGroupByApplication <a href="CHAP008.htm#SSEC001.3">8.1.3</a> <dt>NGroupByNearRingMultiplication <a href="CHAP008.htm#SSEC001.2">8.1.2</a> <dt>NGroupByRightIdealFactor <a href="CHAP008.htm#SSEC001.4">8.1.4</a> <dt>Nicer ways to print a mapping <a href="CHAP004.htm#SECT004">4.4</a> <dt>NIdeal <a href="CHAP008.htm#SSEC006.1">8.6.1</a> <dt>NIdeals <a href="CHAP008.htm#SSEC006.2">8.6.2</a> <dt>NilpotentElements <a href="CHAP002.htm#SSEC022.3">2.22.3</a> <dt>Noetherian quotients <a href="CHAP008.htm#SECT008">8.8</a> <dt>Noetherian quotients for transformation nearrings <a href="CHAP005.htm#SECT005">5.5</a> <dt>NoetherianQuotient <a href="CHAP008.htm#SSEC008.1">8.8.1</a> <dt>NoetherianQuotient, for transformation nearrings <a href="CHAP005.htm#SSEC005.1">5.5. <dt>NontrivialRepresentativesModNormalSubgroup <a href="CHAP001.htm#SSEC010.2">1.10.2</ <dt>Normal subgroups generated by a single element <a href="CHAP001.htm#SECT008">1.8</a> <dt>NSubgroup <a href="CHAP008.htm#SSEC004.1">8.4.1</a> <dt>NSubgroups <a href="CHAP008.htm#SSEC004.2">8.4.2</a> <dt>NumberLibraryNearRings <a href="CHAP003.htm#SSEC001.2">3.1.2</a> <dt>NumberLibraryNearRingsWithOne <a href="CHAP003.htm#SSEC001.5">3.1.5</a> <dt>NumberOfDicksonNearFields <a href="CHAP010.htm#SSEC002.2">10.2.2</a> <dt>NuRadical <a href="CHAP008.htm#SSEC009.1">8.9.1</a> <dt>NuRadicals <a href="CHAP008.htm#SSEC009.2">8.9.2</a> </dl><p> <H2><A NAME="idxO">O</A></H2> <dl> <dt>One <a href="CHAP002.htm#SSEC019.2">2.19.2</a> <dt>OneGeneratedNormalSubgroups <a href="CHAP001.htm#SSEC008.1">1.8.1</a> <dt>Operation tables for groups <a href="CHAP001.htm#SECT002">1.2</a> <dt>Operation tables for nearrings <a href="CHAP002.htm#SECT004">2.4</a> <dt>Operation tables of N-groups <a href="CHAP008.htm#SECT002">8.2</a> <dt>Operations for endo mappings <a href="CHAP004.htm#SECT003">4.3</a> <dt>Operations with ideals <a href="CHAP006.htm#SECT011">6.11</a> <dt>OrbitRepresentativesForPlanarNearRing <a href="CHAP010.htm#SSEC004.2">10.4.2</a> <dt>Other useful functions for groups <a href="CHAP001.htm#SECT012">1.12</a> </dl><p> <H2><A NAME="idxP">P</A></H2> <dl> <dt>Planar nearrings <a href="CHAP010.htm#SECT004">10.4</a> <dt>PlanarNearRing <a href="CHAP010.htm#SSEC004.1">10.4.1</a> <dt>PointsIncidentBlocks <a href="CHAP011.htm#SSEC003.2">11.3.2</a> <dt>PointsOfDesign <a href="CHAP011.htm#SSEC002.1">11.2.1</a> <dt>PolynomialNearRing <a href="CHAP005.htm#SSEC002.4">5.2.4</a> <dt>Predefined groups <a href="CHAP001.htm#SECT001">1.1</a> <dt>PrintAsTerm <a href="CHAP004.htm#SSEC004.2">4.4.2</a> <dt>PrintIncidenceMat <a href="CHAP011.htm#SSEC002.5">11.2.5</a> <dt>PrintTable <a href="CHAP001.htm#SSEC002.1">1.2.1</a> <dt>PrintTable, for N-groups <a href="CHAP008.htm#SSEC002.1">8.2.1</a> <dt>PrintTable, near rings <a href="CHAP002.htm#SSEC004.1">2.4.1</a> <dt>Properties of a design <a href="CHAP011.htm#SECT002">11.2</a> <dt>Properties of endo mappings <a href="CHAP004.htm#SECT002">4.2</a> </dl><p> <H2><A NAME="idxQ">Q</A></H2> <dl> <dt>QuasiregularElements <a href="CHAP002.htm#SSEC022.4">2.22.4</a> </dl><p> <H2><A NAME="idxR">R</A></H2> <dl> <dt>Random ideal elements <a href="CHAP006.htm#SECT006">6.6</a> <dt>Random nearring elements <a href="CHAP002.htm#SECT008">2.8</a> <dt>Random, near ring element <a href="CHAP002.htm#SSEC008.1">2.8.1</a> <dt>Random, near ring ideal element <a href="CHAP006.htm#SSEC006.1">6.6.1</a> <dt>RegularElements <a href="CHAP002.htm#SSEC022.5">2.22.5</a> <dt>RepresentativesModNormalSubgroup <a href="CHAP001.htm#SSEC010.1">1.10.1</a> <dt>RestrictedEndomorphismNearRing <a href="CHAP005.htm#SSEC002.13">5.2.13</a> </dl><p> <H2><A NAME="idxS">S</A></H2> <dl> <dt>Scott length <a href="CHAP001.htm#SECT011">1.11</a> <dt>ScottLength <a href="CHAP001.htm#SSEC011.1">1.11.1</a> <dt>SetSymbols <a href="CHAP002.htm#SSEC005.1">2.5.1</a> <dt>SetSymbolsSupervised <a href="CHAP002.htm#SSEC005.1">2.5.1</a> <dt>Simple nearrings <a href="CHAP006.htm#SECT013">6.13</a> <dt>Size of a nearring <a href="CHAP002.htm#SECT010">2.10</a> <dt>Size of ideals <a href="CHAP006.htm#SECT008">6.8</a> <dt>Size, near ring ideals <a href="CHAP006.htm#SSEC008.1">6.8.1</a> <dt>Size, near rings <a href="CHAP002.htm#SSEC010.1">2.10.1</a> <dt>Special ideal properties <a href="CHAP006.htm#SECT003">6.3</a> <dt>Special properties of a nearring <a href="CHAP002.htm#SECT023">2.23</a> <dt>Special properties of N-groups <a href="CHAP008.htm#SECT007">8.7</a> <dt>Subgroups <a href="CHAP001.htm#SSEC007.1">1.7.1</a> <dt>Subgroups of a group <a href="CHAP001.htm#SECT007">1.7</a> <dt>SubNearRingBySubgroupNC <a href="CHAP002.htm#SSEC017.1">2.17.1</a> <dt>SubNearRings <a href="CHAP002.htm#SSEC015.1">2.15.1</a> <dt>Subnearrings <a href="CHAP002.htm#SECT015">2.15</a> <dt>Supportive functions for groups <a href="CHAP001.htm">1.0</a> <dt>Symbols <a href="CHAP002.htm#SSEC005.2">2.5.2</a> </dl><p> <H2><A NAME="idxT">T</A></H2> <dl> <dt>Testing for ideal properties <a href="CHAP006.htm#SECT002">6.2</a> <dt>The additive group of a nearring <a href="CHAP002.htm#SECT011">2.11</a> <dt>The group a transformation nearring acts on <a href="CHAP005.htm#SECT003">5.3</a> <dt>The nearring library <a href="CHAP003.htm">3.0</a> <dt>Transformation nearrings <a href="CHAP005.htm">5.0</a> <dt>Transformation nearrings and other nearrings <a href="CHAP005.htm#SECT004">5.4</a> <dt>TransformationNearRing <a href="CHAP005.htm#SSEC002.2">5.2.2</a> <dt>TransformationNearRingByAdditiveGenerators <a href="CHAP005.htm#SSEC001.2">5.1.2</a> <dt>TransformationNearRingByGenerators <a href="CHAP005.htm#SSEC001.1">5.1.1</a> <dt>TWGroup <a href="CHAP001.htm#SSEC001.1">1.1.1</a> <dt>TypeOfNGroup <a href="CHAP008.htm#SSEC007.7">8.7.7</a> </dl><p> <H2><A NAME="idxU">U</A></H2> <dl> <dt>Units of a nearring <a href="CHAP002.htm#SECT020">2.20</a> </dl><p> <H2><A NAME="idxW">W</A></H2> <dl> <dt>WdNearRing <a href="CHAP010.htm#SSEC005.1">10.5.1</a> <dt>Weakly divisible nearrings <a href="CHAP010.htm#SECT005">10.5</a> <dt>Working with the points and blocks of a design <a href="CHAP011.htm#SECT003">11.3</a> </dl><p> <H2><A NAME="idxZ">Z</A></H2> <dl> <dt>Zerosymmetric mappings <a href="CHAP005.htm#SECT006">5.6</a> <dt>ZeroSymmetricCompatibleFunctionNearRing <a href="CHAP005.htm#SSEC002.9">5.2.9</a> <dt>ZeroSymmetricElements <a href="CHAP002.htm#SSEC022.1">2.22.1</a> <dt>ZeroSymmetricPart, for transformation nearrings <a href="CHAP005.htm#SSEC006.1">5.6.1< </dl><p> [<a href="chapters.htm">Up</a>]<p> <P> <address>SONATA manual<br>September 2025 </address></body></html>
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2026-04-02