73.6 ConjugationXMod

ConjugationXMod( R [,S] )

This construction returns the crossed module whose source S is a normal subgroup of the range R, the boundary is the inclusion map, the group of automorphisms is the inner automorphism group of S, and the action maps an element of r in R to conjugation of S by r. The default value for S is R.

    gap> s4 := Group( (1,2,3,4), (1,2) );;
    gap> a4 := Subgroup( s4, [ (1,2,3), (2,3,4) ] );;
    gap> k4 := Subgroup( a4, [ (1,2)(3,4), (1,3)(2,4) ] );;
    gap> s4.name := "s4";;  a4.name := "a4";;  k4.name := "k4";;
    gap> CX := ConjugationXMod( a4, k4 );
    Crossed module [k4->a4] 

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