<
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title>SONATA : a GAP
4 package - Index </
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<
h1><
font face=
"Gill Sans,Helvetica,Arial">SONATA</
font> : a <
font face=
"Gill Sans,Helvetica,Arial">GAP</
font>
4 package - Index </
h1>
<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#SECT004">
3.
4</a>
<
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.htm#SSEC005.2">
5.
5.
2</a>
<
dt>CongruenceNoetherianQuotientForInnerAutomorphismNearRings , for inner automorphism
nearrings <a href="CHAP005.htm#SSEC005.3">5.5.3</a>
<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#SECT003">9.3</a>
<dt>Fixed-point-free automorphism groups and Frobenius groups <a href="CHAP009.htm#SECT001">9.1</a>
<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">3.3.1</a>
<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">5.5.1</a>
<dt>NontrivialRepresentativesModNormalSubgroup <a href="CHAP001.htm#SSEC010.2">1.10.2</a>
<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</a>
</dl><p>
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<address>SONATA manual<br>September 2025
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