Cat1XMod( X )
This function acts as the functor from the category of crossed modules
to the category of cat1-groups. A permutation representation of the
semidirect product R semidirect S is constructed for G. See
section refSemidirectCat1XMod for a version where G is a
semidirect product group. The example uses the crossed module CX
constructed in section
refConjugationXMod.
gap> CX;
Crossed module [k4->a4]
gap> CCX := Cat1XMod( CX );
cat1-group [a4.k4 ==> a4]
gap> Cat1Print( CCX );
cat1-group [a4.k4 ==> a4] :-
: source group has generators:
[ (2,4,3)(5,6,7), (2,3,4)(6,7,8), (1,2)(3,4), (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:
[ ( 2, 4, 3)( 5, 6, 7), ( 2, 3, 4)( 6, 7, 8) ]
: 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:
[ (1,2)(3,4), (1,3)(2,4) ]
: associated crossed module is Crossed module [k4->a4]
GAP 3.4.4