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
GAP 3.4.4