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