73.28 DirectProduct for crossed modules

XModOps.DirectProduct( X,Y )

The direct product of crossed modules X,Y has as source and range the direct products of the sources and ranges of X and Y. The boundary map is the product of the two boundaries. The range of X acts trivially on the source of Y and conversely. Because the standard DirectProduct function requires the two parameters to be groups, the XModOps. prefix must be used (at least for GAP3.4.3).

    gap> DX := XModOps.DirectProduct( CX, CX );
    Crossed module [v4xv4->a4xa4]
    gap> XModPrint( DX );

    Crossed module [v4xv4->a4xa4] :- 
    : Source group v4xv4 has generators:
      [ (1,2)(3,4), (1,3)(2,4), (5,6)(7,8), (5,7)(6,8) ]
    : Range group = a4xa4 has generators:
      [ (1,2,3), (2,3,4), (5,6,7), (6,7,8) ]
    : Boundary homomorphism maps source generators to:
      [ (1,2)(3,4), (1,3)(2,4), (5,6)(7,8), (5,7)(6,8) ]
    : Action homomorphism maps range generators to automorphisms:
      (1,2,3) --> { source gens -->
          [ (1,4)(2,3), (1,2)(3,4), (5,6)(7,8), (5,7)(6,8) ] }
      (2,3,4) --> { source gens -->
          [ (1,3)(2,4), (1,4)(2,3), (5,6)(7,8), (5,7)(6,8) ] }
      (5,6,7) --> { source gens -->
          [ (1,2)(3,4), (1,3)(2,4), (5,8)(6,7), (5,6)(7,8) ] }
      (6,7,8) --> { source gens -->
          [ (1,2)(3,4), (1,3)(2,4), (5,7)(6,8), (5,8)(6,7) ] }
      These 4 automorphisms generate the group of automorphisms. 

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