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Magma
Computer • algebra
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Overview
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
Hirsch Number and Pr{üfer Rank
HasFiniteRank (G) : GrpMat -> BoolElt
HirschNumber (G) : GrpMat -> RngIntElt
HasFiniteIndex (G, H) : GrpMat, GrpMat -> BoolElt
PrueferRankBound (G) : GrpMat -> BoolElt
Other Properties of Linear Groups
IsCompletelyReducible(G : parameters) : GrpMat -> BoolElt
CompletelyReduciblePart (G) : GrpMat -> GrpMat, GrpMatElt
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
RecogniseAbelian (G) : GrpMat -> GrpGPC, Map, Map
SylowSystem(G : parameters) : GrpMat[FldFin] -> []
IsIrreducibleFiniteNilpotent(G : parameters): GrpMat -> BoolElt, Any
IsPrimitiveFiniteNilpotent(G : parameters): GrpMat -> BoolElt, Any
Examples
Example
GrpMatInf_IsFiniteMatrixGroupFQ (H67E1)
Example
GrpMatInf_IsFiniteMatrixGroupFF (H67E2)
Example
GrpMatInf_IsFiniteMatrixGroupFF (H67E3)
Example
GrpMatInf_IsFiniteMatrixGroupFF (H67E4)
Example
GrpMatInf_IsFiniteMatrixGroupFF (H67E5)
Example
GrpMatInf_IsFiniteMatrixGroup (H67E6)
Example
GrpMatInf_IsFiniteMatrixGroupF (H67E7)
Example
GrpMatInf_IsFiniteMatrixGroupF (H67E8)
Example
GrpMatInf_IsFiniteMatrixGroupF (H67E9)
Example
GrpMatInf_IsFiniteMatrixGroupF (H67E10)
Example
GrpMatInf_IsNilpotentMatrixGroupF (H67E11)
Example
GrpMatInf_IsNilpotentMatrixGroupF (H67E12)
Example
GrpMatInf_IsNilpotentMatrixGroupF (H67E13)
Example
GrpMatInf_IsNilpotentMatrixGroupF (H67E14)
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V2.28, 28 February 2025