73.12 IsRModule for groups

IsRModule( Rmod )

IsRModuleRecord( Rmod )

An R-module consists of a permutation group R with an action alpha : R to A where A is a group of automorphisms of an abelian group M. When R is not specified, the function AutomorphismPair is automatically called to construct it.

This structure is implemented here as a record Rmod with fields:

Rmod.module, & the abelian group M,
Rmod.perm, & the group R,
Rmod.auto, & the action group A,
Rmod.isRModule, & set true.

The IsRModule distributor calls this function when the parameter is a record but not a crossed module.

    gap> k4gen := k4.generators;;
    gap> k4im := [ (1,3)(2,4), (1,4)(2,3) ];;
    gap> a := GroupHomomorphismByImages( k4, k4, k4gen, k4im );;
    gap> Ak4 := Group( a );;
    gap> R := rec( );;
    gap> R.module := k4;;
    gap> R.auto := Ak4;;
    gap> IsRModule( R );
    true
    gap> RecFields( R );
    [ "module", "auto", "perm", "isRModule" ]
    gap> R.perm;
    PermSubAut(v4)   

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