Introduction
Overview
Finding Elements with Prescribed Properties RandomElementOfOrder(G, order : parameters) : GrpMat, order-> BoolElt, GrpMatElt, GrpSLPElt, BoolElt RandomElementOfNormalClosure(G, N): Grp -> GrpElt CentralOrder(g : parameters) : GrpMatElt -> RngIntElt, BoolElt
Monte-Carlo Algorithms for Subgroups CentraliserOfInvolution(G, g : parameters) : GrpMat,GrpMatElt -> GrpMat CentraliserOfInvolution(G, g, w : parameters) : GrpMat,GrpMatElt, GrpSLPElt -> GrpMat, [] AreInvolutionsConjugate(G, x, wx, y, wy : parameters) : GrpMat,GrpMatElt, GrpSLPElt, GrpMatElt, GrpSLPElt -> BoolElt, GrpMatElt, GrpSLPElt DerivedGroupMonteCarlo (G : parameters) : GrpMat -> GrpMat IsProbablyPerfect(G : parameters): Grp -> BoolElt Example GrpMatFF_IsProbablyPerfect (H53E1)
Aschbacher Reduction
Primitivity IsPrimitive(G: parameters) : GrpMat -> BoolElt ImprimitiveBasis (G) : GrpMat -> SeqEnum Blocks(G) : GrpMat -> SeqEnum BlocksImage(G) : GrpMat -> GrpPerm ImprimitiveAction(G, g) : GrpMat, GrpMatElt -> GrpPermElt Example GrpMatFF_IsPrimitive (H53E2)
Semilinearity IsSemiLinear(G) : GrpMat -> BoolElt DegreeOfFieldExtension(G) : GrpMat -> RngIntElt CentralisingMatrix(G) : GrpMat -> AlgMatElt FrobeniusAutomorphisms(G) : GrpMat -> SeqEnum WriteOverLargerField(G) : GrpMat -> GrpMat, GrpAb, SeqEnum Example GrpMatFF_Semilinearity (H53E3)
Tensor Products IsTensor(G: parameters) : GrpMat -> BoolElt TensorBasis(G) : GrpMat -> GrpMatElt TensorFactors(G) : GrpMat -> GrpMat, GrpMat IsProportional(X, k) : Mtrx, RngIntElt -> BoolElt, Tup Example GrpMatFF_Tensor (H53E4)
Tensor-induced Groups IsTensorInduced(G : parameters) : GrpMat -> BoolElt TensorInducedBasis(G) : GrpMat -> GrpMatElt TensorInducedPermutations(G) : GrpMat -> SeqEnum TensorInducedAction(G, g) : GrpMat, GrpMatElt -> GrpPermElt Example GrpMatFF_TensorInduced (H53E5)
Normalisers of Extraspecial r-groups and Symplectic 2-groups IsExtraSpecialNormaliser(G) : GrpMat -> BoolElt ExtraSpecialParameters(G) : GrpMat -> [RngIntElt, RngIntElt] ExtraSpecialGroup(G) : GrpMat -> GrpMat ExtraSpecialNormaliser(G) : GrpMat -> SeqEnum ExtraSpecialAction(G, g) : GrpMat, GrpMatElt -> GrpMatElt ExtraSpecialBasis(G) : GrpMat -> GrpMatElt Example GrpMatFF_ExtraSpecialNormaliser (H53E6)
Writing Representations over Subfields IsOverSmallerField (G: parameters) : GrpMat -> BoolElt, GrpMat IsOverSmallerField (G, k: parameters) : GrpMat -> BoolElt, GrpMat SmallerField(G) : GrpMat -> FLdFin SmallerFieldBasis (G) : GrpMat -> GrpMatElt SmallerFieldImage (G, g) : GrpMat, GrpMatElt -> GrpMatElt Example GrpMatFF_IsOverSmallerField (H53E7) WriteOverSmallerField(G, F) : GrpMat, FldFin -> GrpMat, Map Example GrpMatFF_WriteOverSmallerField (H53E8)
Decompositions with Respect to a Normal Subgroup SearchForDecomposition(G, S) : GrpMat, [GrpMatElt] -> BoolElt
Accessing the Decomposition Information
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