73.57 Cat1XMod

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]

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GAP 3.4.4
April 1997