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
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X k4 ==> a4] gap> Cat1Print( SCX );cat1-group [a4
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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