Construction of Congruence Homomorphisms
CongruenceImage(G : parameters) : GrpMat -> GrpMat,HomGrp, []
Testing Finiteness
IsFinite(G : parameters) : GrpMat -> BoolElt, RngIntElt
IsomorphicCopy(G : parameters) : GrpMat -> BoolElt, GrpMat, HomGrp
Order(G : parameters) : GrpMat -> RngIntElt
Deciding Virtual Properties of Linear Groups
IsSolubleByFinite(G : parameters) : GrpMat -> BoolElt
IsPolycyclicByFinite(G : parameters) : GrpMat -> BoolElt
IsNilpotentByFinite(G : parameters) : GrpMat -> BoolElt
IsAbelianByFinite(G : parameters) : GrpMat -> BoolElt
IsCentralByFinite(G : parameters) : GrpMat -> BoolElt
Other Properties of Linear Groups
IsCompletelyReducible(G : parameters) : GrpMat -> BoolElt
IsUnipotent(G) : GrpMat -> BoolElt, GrpMatElt
IsNilpotent(G) : GrpMat -> BoolElt
IsSoluble(G : parameters) : GrpMat -> BoolElt
IsPolycyclic(G : parameters) : GrpMat -> BoolElt
HasFiniteOrder (g : parameters ) : GrpMatElt -> BoolElt, RngIntElt
Other Functions for Nilpotent Matrix Groups
SylowSystem(G : parameters) : GrpMat[FldFin] -> []
IsIrreducibleFiniteNilpotent(G : parameters): GrpMat -> BoolElt, Any
IsPrimitiveFiniteNilpotent(G : parameters): GrpMat -> BoolElt, Any
Examples
Example GrpMatInf_IsFiniteMatrixGroupFQ (H61E1)
Example GrpMatInf_IsFiniteMatrixGroupFF (H61E2)
Example GrpMatInf_IsFiniteMatrixGroupFF (H61E3)
Example GrpMatInf_IsFiniteMatrixGroupFF (H61E4)
Example GrpMatInf_IsFiniteMatrixGroupFF (H61E5)
Example GrpMatInf_IsFiniteMatrixGroup (H61E6)
Example GrpMatInf_IsFiniteMatrixGroupF (H61E7)
Example GrpMatInf_IsFiniteMatrixGroupF (H61E8)
Example GrpMatInf_IsNilpotentMatrixGroupF (H61E9)
Example GrpMatInf_IsNilpotentMatrixGroupF (H61E10)
Example GrpMatInf_IsNilpotentMatrixGroupF (H61E11)
Bibliography
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Version: V2.19 of
Wed Apr 24 15:09:57 EST 2013