# The GAP 4 Manual - Full Index S

_ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

s_N R 18.4
SameBlock R 69.9.2
SandwichMatrixOfReesMatrixSemigroup R 49.6.7
SandwichMatrixOfReesZeroMatrixSemigroup R 49.6.7
save R 3.10
SaveOnExitFile R 6.7.3
SaveWorkspace R 3.10.1
Saving a Pc Group R 44.6
Saving and Loading a Workspace R 3.10
saving on exit R 6.7
ScalarProduct, for characters R 70.8.5
ScanMOC R 69.21.4
Schreier R 46.3
Schreier-Sims, random R 41.6
SchreierTransversal N 4.2.1
SchreierTreeDepth N 4.2.11
Schur Covers and Multipliers R 37.23
Schur multiplier R 37.23
SchurCover R 37.23.2
scope R 4.8
ScriptFromString R 68.10.2
Searching for Homomorphisms R 38.9
SecHMSM R 26.7.8
secondary subgroup generators R 46.11
SecondsDMYhms R 26.7.10
SeekPositionStream R 10.3.10
Selecting a Different MeatAxe R 67.2
Selection Functions R 48.5
Semidirect Products R 47.2
SemidirectProduct R 47.2.1
SemiEchelonBasis R 59.8.8
SemiEchelonBasisNC R 59.8.8
SemiEchelonMat R 24.9.1
SemiEchelonMatDestructive R 24.9.2
SemiEchelonMats R 24.9.4
SemiEchelonMatsDestructive R 24.9.5
SemiEchelonMatTransformation R 24.9.3
semigroup R 49.0
Semigroup R 49.0 R 49.0
SemigroupByGenerators R 49.0
SemigroupByMultiplicationTable R 49.0
SemigroupIdealByGenerators R 49.2.1
SemigroupOfRewritingSystem R 51.5.3
Semigroups R 49.0
semiregular R 39.9
Semisimple Lie Algebras and Root Systems R 61.7
SemiSimpleType R 61.7.1
sequence, Bernoulli R 17.1
sequence, Fibonacci R 17.3
sequence, Lucas R 17.3
Series of Ideals R 61.4
Set R 28.2.5
set difference, of collections R 28.4
Set Operations via Boolean Lists R 22.2
set stabilizer R 39.4
SetAssertionLevel R 7.5.1
SetCommutator R 44.4.4
SetConjugate R 44.4.3
SetCrystGroupDefaultAction R 42.6.2
SetElmWPObj E 7.3.1
SetEntrySCTable R 60.3.2
SetFilterObj P 3.4.2
SetHashEntry N 2.7.3
SetHashEntryAtLastIndex N 2.7.2
SetHelpViewer R 2.3.1
SetIndeterminateName R 64.1.4
SetInfoLevel R 7.4.3
SetName R 12.8.1
SetParent R 30.7.1
SetPower R 44.4.5
SetPrintFormattingStatus R 10.4.8
SetRecursionTrapInterval R 7.10.1
Sets T 3.4
sets R 21.19
Sets R 12.3
Sets of Subgroups R 37.18
setter R 13.6
setter, of an attribute T 8.1
Setter R 13.6.2
Setter and Tester for Attributes R 13.6
SetX R 21.21.2
ShallowCopy T 9.7
ShallowCopy R 12.7.1
ShallowCopy, for lists R 21.7
ShiftedCoeffs R 23.6.6
ShiftedPadicNumber R 66.1.4
Shifting and Trimming Coefficient Lists R 23.4
short vectors spanning a lattice R 25.3 R 70.10
ShortestVectors R 25.4.2
ShortLexOrdering R 29.3.6
ShowArgument R 7.1.2
ShowArguments R 7.1.1
ShowDetails R 7.1.3
ShowImpliedFilters R 13.2.3
ShowMethods R 7.1.4
ShowOtherMethods R 7.1.5
ShrinkCoeffs R 23.6.7
ShrinkRowVector R 23.4.3
Sift, for chains of subgroups N 5.0
SiftedPcElement R 43.5.8
SiftedPermutation R 41.9.11
SiftedVector R 59.8.12
SiftOneLevel, for chains of subgroups N 5.0
SiftOneLevel, for subgroup transversals N 4.1.2
Sigma R 15.4.1
sign, of an integer R 14.1
Sign and Cycle Structure R 40.3
SignInt R 14.1.7
SignPartition R 17.2.23
SignPerm R 40.3.1
SimpleLieAlgebra R 61.2.6
SimpleSystem R 61.7.11
SimplifiedFpGroup R 46.2 R 46.2.1
SimplifyPresentation R 46.7.2
SimsNo R 48.9.5
SimultaneousEigenvalues R 24.13.4
SingleCollector R 44.4.2
singlequote character R 26.1
singlequotes R 26.0
Size, for character tables R 69.8
Size, for groups with pcgs R 43.16
size, of a list or collection R 28.3
Size R 28.3.6
SizeBlist R 22.1.3
SizeConsiderFunction R 37.20.4
SizeNumbersPerfectGroups R 48.8.6
SizeOfChainOfGroup N 5.0
SizeOfFieldOfDefinition R 70.15.3
SizesCentralizers R 69.8.6
SizesConjugacyClasses R 69.8.7
SizeScreen R 6.11 R 6.11.1
SizesPerfectGroups R 48.8.1
SizeStabChain R 41.9.3
SL R 48.2.2
Small Groups R 48.7
smaller, rational functions R 64.3.2
smaller, pcwords R 44.2.1
smaller, nonassociative words R 34.2.2
smaller, elements of finitely presented groups R 45.2.2
smaller, associative words R 35.3.2
smaller or equal R 4.11.2
smaller test R 4.11.2
SmallerDegreePermutationRepresentation R 41.2.2
SmallestGeneratorPerm R 40.1.2
SmallestMovedPoint R 40.2.1
SmallestRootInt R 14.1.10
SmallGeneratingSet R 37.21.4
SmallGroup R 48.7.1
SmallGroupsInformation R 48.7.8
Smash MeatAxe Flags R 67.9
SmithNormalFormIntegerMat R 25.1.6
SmithNormalFormIntegerMatInverseTransforms R 25.1.6
SmithNormalFormIntegerMatTransforms R 25.1.6
SMTX.AbsoluteIrreducibilityTest R 67.8.8
SMTX.AlgEl R 67.9.2
SMTX.AlgElCharPol R 67.9.4
SMTX.AlgElCharPolFac R 67.9.5
SMTX.AlgElMat R 67.9.3
SMTX.AlgElNullspaceDimension R 67.9.7
SMTX.AlgElNullspaceVec R 67.9.6
SMTX.CentMat R 67.9.8
SMTX.CentMatMinPoly R 67.9.9
SMTX.CompleteBasis R 67.8.11
SMTX.Getter R 67.8.6
SMTX.GoodElementGModule R 67.8.2
SMTX.IrreducibilityTest R 67.8.7
SMTX.MatrixSum R 67.8.10
SMTX.MinimalSubGModule R 67.8.9
SMTX.MinimalSubGModules R 67.8.4
SMTX.RandomIrreducibleSubGModule R 67.8.1
SMTX.Setter R 67.8.5
SMTX.SortHomGModule R 67.8.3
SMTX.Subbasis R 67.9.1
SNFChouCollins R 25.1.2
SNFLLLDriven R 25.1.2
SNFNormDriven R 25.1.2
SNFofREF R 25.1.3
SO R 48.2.7
Socle R 37.11.10
SocleTypePrimitiveGroup R 41.4.2
Solaris R 73.3
SolutionMat R 24.6.5
SolutionMatDestructive R 24.6.6
Some Remarks about Character Theory in GAP R 69.1
Some Special Algebras R 60.4
Something T 7.4
Sort R 21.18.1
Sorted Character Tables R 69.18
sorted list R 21.17
Sorted Lists and Sets R 21.19
Sorted Lists as Collections R 28.2
SortedCharacters R 69.18.2
SortedCharacterTable R 69.18.4
SortedList R 28.2.4
SortedSparseActionHomomorphism R 39.6.3
SortedTom R 68.5.1
Sortex R 21.18.3
Sorting Lists R 21.18
Sorting Tables of Marks R 68.5
SortingPerm R 21.18.4
SortParallel R 21.18.2
Source N 3.2.5
Source R 31.2.8
SourceElt N 3.2.2
Sp R 48.2.5
SP R 48.2.5
space R 4.4
Sparse hash tables N 2.6
SparseActionHomomorphism R 39.6.3
SparseCartanMatrix R 61.7.16
SparseHashTable N 2.6.1
SparseIntKey N 2.4.3
special character sequences R 26.1
Special Characters R 26.1
Special Filenames R 9.5
Special Generating Sets R 37.21
Special Pcgs R 43.13
SpecialLinearGroup R 48.2.2
SpecialOrthogonalGroup R 48.2.7
SpecialPcgs, attribute R 43.13.2
SpecialUnitaryGroup R 48.2.4
Specific and Parametrized Subgroups R 37.11
Specific Methods for Subgroup Lattice Computations R 37.20
SplitCharacters R 69.14.7
SplitExtension R 44.8.6
SplitExtensions R 44.8.10
SplitString R 26.5.6
SplittingField R 64.4.13
Sqrt R 30.12.5
square root, of an integer R 14.1
SquareRoots R 33.4.13
SSortedList R 28.2.5
StabChain R 41.7.1
StabChainBaseStrongGenerators R 41.7.4
StabChainImmutable R 41.7.1
StabChainMutable R 41.7.1
StabChainOp R 41.7.1
StabChainOptions R 41.7.2
Stabiliser chain subgroups N 5.1
Stabilizer R 39.4.2
Stabilizer Chain Records R 41.8
Stabilizer Chains R 41.5
Stabilizer Chains E 8.0
Stabilizer Chains for Automorphisms Acting on Enumerators E 8.3
StabilizerOfExternalSet R 39.11.10
StabilizerPcgs R 43.15.1
Stabilizers R 39.4
Standalone Programs in a GAP Package E 4.4
Standard Generators of Groups R 68.10
StandardAssociate R 54.5.5
StandardGeneratorsFunctions R 68.10.3
StandardGeneratorsInfo, for groups R 68.10.1
StandardGeneratorsInfo, for tables of marks R 68.11.5
StandardGeneratorsOfGroup R 68.10.5
Standardization of coset tables R 45.6
StandardizeTable R 45.6.2
StarCyc R 18.5.2
Starting and Leaving GAP T 2.1
starting GAP T 2.1
Statements R 4.13
StateRandom R 28.6.2
Stirling number of the first kind R 17.1
Stirling number of the second kind R 17.1
Stirling1 R 17.1.5
Stirling2 R 17.1.6
StoreFusion R 71.2.4
Storing Normal Subgroup Information R 69.22
Straight Line Program Elements R 35.9
Straight Line Programs R 35.8
StraightLineProgElm R 35.9.2
StraightLineProgGens R 35.9.3
StraightLineProgram R 35.8.2
StraightLineProgramNC R 35.8.2
StraightLineProgramsTom R 68.11.2
StratMeetPartition E 8.2.1
Streams R 10.0
StreamsFamily R 10.1.9
StretchImportantSLPElement R 35.9.5
strictly sorted list R 21.17
String R 26.5.1
String, for cyclotomics R 18.1
String Streams R 10.7
StringDate R 26.7.6
StringOfResultOfStraightLineProgram R 35.8.6
StringPP R 26.5.3
strings, lexicographic ordering of R 26.4.2
strings, equality of R 26.4.1
strings, inequality of R 26.4.1
strings T 3.1
Strings and Characters R 26.0
StringTime R 26.7.9
StrongGeneratorsStabChain R 41.9.4
StrongGens N 5.1.3
StronglyConnectedComponents R 32.4.5
Struct R 30.3.1
StructByGenerators R 30.3.4
StructuralCopy R 12.7.2
StructuralCopy T 9.7
StructuralCopy, for lists R 21.7
structure constant R 69.10
StructureConstantsTable R 59.6.4
StructWithGenerators R 30.3.5
SU R 48.2.4
Subalgebra R 60.5.1
SubAlgebraModule R 60.10.16
SubalgebraNC R 60.5.2
Subalgebras R 60.5
SubalgebraWithOne R 60.5.3
SubalgebraWithOneNC R 60.5.4
Subdirect Products R 47.3
SubdirectProduct R 47.3.1
Subdomains R 30.8
Subdomains T 7.7
Subfield R 56.2.1
SubfieldNC R 56.2.1
Subfields R 56.2.10
Subfields of Fields R 56.2
Subgroup R 37.3.1
subgroup fusions R 71.2
subgroup generators tree R 46.11
Subgroup Lattice R 37.19
Subgroup Presentations R 46.3
Subgroup Series R 37.16
SubgroupByPcgs R 43.7.9
SubgroupNC R 37.3.1
SubgroupOfWholeGroupByCosetTable R 45.7.2
SubgroupOfWholeGroupByQuotientSubgroup R 45.12.1
SubgroupProperty R 41.11.1
Subgroups, as Stabilizers T 5.3
subgroups, polyhedral R 69.10
Subgroups R 37.3
Subgroups characterized by prime powers R 37.13
Subgroups of Polycyclic Groups - Canonical Pcgs R 43.8
Subgroups of Polycyclic Groups - Induced Pcgs R 43.7
SubgroupsSolvableGroup R 37.20.3
sublist, access R 21.3.2
sublist, operation R 21.3.3
sublist R 21.3
sublist, assignment R 21.4.2
sublist assignment, operation R 21.4.3
Submagma R 33.2.7
SubmagmaNC R 33.2.7
SubmagmaWithInverses R 33.2.9
SubmagmaWithInversesNC R 33.2.9
SubmagmaWithOne R 33.2.8
SubmagmaWithOneNC R 33.2.8
Submodule R 55.2.1
SubmoduleNC R 55.2.2
Submodules R 55.2
Submonoid R 50.0
SubmonoidNC R 50.0
SubnearAdditiveGroup R 53.2.9
SubnearAdditiveGroupNC R 53.2.9
SubnearAdditiveMagma R 53.2.7
SubnearAdditiveMagmaNC R 53.2.7
SubnearAdditiveMagmaWithZero R 53.2.8
SubnearAdditiveMagmaWithZeroNC R 53.2.8
SubnormalSeries R 37.16.4
Subring R 54.1.8
SubringNC R 54.1.8
SubringWithOne R 54.3.5
SubringWithOneNC R 54.3.5
Subroutines for the Construction of Class Fusions R 71.5
Subroutines for the Construction of Power Maps R 71.4
subsection mark-up E 2.5
Subsemigroup R 49.0
SubsemigroupNC R 49.0
subset test, for collections R 28.4
subsets R 17.2
Subsomething T 7.7
SubsomethingNC T 7.7
Subspace R 59.1.2
SubspaceNC R 59.1.2
Subspaces R 59.3.1
SubstitutedWord R 35.4.5
SubsTom R 68.7.1
Substruct R 30.8.1
SubstructNC R 30.8.2
SubSyllables R 35.5.4
subtract, a set from another R 21.19
SubtractBlist R 22.3.4
subtraction, rational functions R 64.2.1
subtraction, matrix and scalar R 24.2.3
subtraction, matrices R 24.2.3
subtraction R 4.12.1
subtraction, vectors R 23.1.3
subtraction, vector and scalar R 23.1.3
subtraction, scalar and vector R 23.1.3
subtraction, scalar and matrix list R 24.2.12
subtraction, scalar and matrix R 24.2.3
SubtractSet R 21.19.8
Subword R 35.4.3
Successors R 32.2.9
Suitability for Compilation R 3.7
Sum R 21.20.23
Sum and Intersection of Pcgs R 43.12
SumFactorizationFunctionPcgs R 43.12.1
SumIntersectionMat R 24.10.4
SumX R 21.21.3
SupersolvableResiduum R 37.11.11
superuser R 74.2
SupportedCharacterTableInfo R 69.3.3
Suppressing Indexing and Labelling of a Section and Resolving Label Clashes E 2.3
SurjectiveActionHomomorphismAttr R 39.11.17
SuzukiGroup R 48.1.10
Sylow Subgroups and Hall Subgroups R 37.12
SylowComplement R 37.12.2
SylowSubgroup R 37.12.1
SylowSystem R 37.12.4
Symbols R 4.3
Symmetric and Alternating Groups R 41.3
symmetric group, powermap R 17.2
symmetric relation R 32.2
SymmetricClosureBinaryRelation R 32.4.2
SymmetricGroup R 48.1.8
SymmetricParentGroup R 41.3.5
SymmetricParts R 70.11.2
SymmetricPowerOfAlgebraModule R 61.14.3
symmetrizations, symplectic R 70.11
symmetrizations, orthogonal R 70.11
Symmetrizations R 70.11.1
Symmetrizations of Class Functions R 70.11
SymplecticComponents R 70.11.5
SymplecticGroup R 48.2.5
syntax errors R 6.1
System V R 73.3
SysV R 73.3
Sz R 48.1.10

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