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MATRIX GROUPS OVER INFINITE FIELDS

 
Acknowledgements
 
Overview
 
Construction of Congruence Homomorphisms
 
Testing Finiteness
 
Deciding Virtual Properties of Linear Groups
 
Other Properties of Linear Groups
 
Other Functions for Nilpotent Matrix Groups
 
Examples
 
Bibliography







DETAILS

 
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

 
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 Mon Dec 17 14:40:36 EST 2012