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 (H68E1)
      Example GrpMatInf_IsFiniteMatrixGroupFF (H68E2)
      Example GrpMatInf_IsFiniteMatrixGroupFF (H68E3)
      Example GrpMatInf_IsFiniteMatrixGroupFF (H68E4)
      Example GrpMatInf_IsFiniteMatrixGroupFF (H68E5)
      Example GrpMatInf_IsFiniteMatrixGroup (H68E6)
      Example GrpMatInf_IsFiniteMatrixGroupF (H68E7)
      Example GrpMatInf_IsFiniteMatrixGroupF (H68E8)
      Example GrpMatInf_IsFiniteMatrixGroupF (H68E9)
      Example GrpMatInf_IsFiniteMatrixGroupF (H68E10)
      Example GrpMatInf_IsNilpotentMatrixGroupF (H68E11)
      Example GrpMatInf_IsNilpotentMatrixGroupF (H68E12)
      Example GrpMatInf_IsNilpotentMatrixGroupF (H68E13)
      Example GrpMatInf_IsNilpotentMatrixGroupF (H68E14)

 
Bibliography

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