SemidirectCat1XMod( X )
This function is similar to the previous one, but a permutation representation for R semidirect S is not constructed.
gap> Unbind( CX.cat1 );
gap> SCX := SemidirectCat1XMod( CX );
cat1-group [a4 |X k4 ==> a4]
gap> Cat1Print( SCX );
cat1-group [a4
|X k4 ==> a4] :-
: source group has generators:
[ SemidirectProductElement( (1,2,3), GroupHomomorphismByImages( k4,
k4, [(1,3)(2,4), (1,4)(2,3)], [(1,2)(3,4), (1,3)(2,4)] ), () ),
SemidirectProductElement( (2,3,4), GroupHomomorphismByImages( k4,
k4, [(1,4)(2,3), (1,2)(3,4)], [(1,2)(3,4), (1,3)(2,4)] ), () ),
SemidirectProductElement( (), IdentityMapping( k4 ), (1,2)(3,4) ),
SemidirectProductElement( (), IdentityMapping( k4 ), (1,3)(2,4) ) ]
: range group has generators:
[ (1,2,3), (2,3,4) ]
: tail homomorphism maps source generators to:
[ (1,2,3), (2,3,4), (), () ]
: head homomorphism maps source generators to:
[ (1,2,3), (2,3,4), (1,2)(3,4), (1,3)(2,4) ]
: range embedding maps range generators to:
[ SemidirectProductElement( (1,2,3), GroupHomomorphismByImages( k4,
k4, [(1,3)(2,4), (1,4)(2,3)], [(1,2)(3,4), (1,3)(2,4)] ), () ),
SemidirectProductElement( (2,3,4), GroupHomomorphismByImages( k4,
k4, [(1,4)(2,3), (1,2)(3,4)], [(1,2)(3,4), (1,3)(2,4)] ), () ) ]
: kernel has generators:
[ (1,2)(3,4), (1,3)(2,4) ]
: boundary homomorphism maps generators of kernel to:
[ (1,2)(3,4), (1,3)(2,4) ]
: kernel embedding maps generators of kernel to:
[ SemidirectProductElement( (), IdentityMapping( k4 ), (1,2)(3,4) ),
SemidirectProductElement( (), IdentityMapping( k4 ), (1,3)(2,4) ) ]
: associated crossed module is Crossed module [k4->a4]
GAP 3.4.4