73.11 TrivialActionXMod

TrivialActionXMod( f )

For a crossed module to have trivial action, the axioms require the source to be abelian and the image of the boundary to lie in the centre of the range. A homomorphism f can act as the boundary map when these conditions are satisfied.

    gap> imf := [ (1,3)(2,4), (1,3)(2,4) ];;
    gap> f := GroupHomomorphismByImages( k4, d8, genk4, imf );;
    gap> TX := TrivialActionXMod( f );
    Crossed module [v4->d8]
    gap> XModPrint( TX );

Crossed module [v4->d8] :- : Source group has parent ( s4 ) and has generators: [ (1,2)(3,4), (1,3)(2,4) ] : Range group has parent ( s4 ) and has generators: [ (1,2,3,4), (1,3) ] : Boundary homomorphism maps source generators to: [ (1,3)(2,4), (1,3)(2,4) ] The automorphism group is trivial

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GAP 3.4.4
April 1997