73.58 SemidirectCat1XMod

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]   

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GAP 3.4.4
April 1997