73.43 InnerAutomorphism of a crossed module

InnerAutomorphism( X, r )

Each element r of X.range determines an automorphism of X in which the automorphism of X.source is given by the image of X.action on r and the automorphism of X.range is conjugation by r. The command InnerAutomorphism( X, r ); does not work with version 3 of GAP.

    gap> g := Elements( q8 )[8];
    (1,8,3,6)(2,5,4,7)
    gap> psi := XModOps.InnerAutomorphism( subSX, g );
    Morphism of crossed modules <[c4->q8] >-> [c4->q8]>
    gap> XModMorphismPrint( psi );
    Morphism of crossed modules :- 
    : Source = Crossed module [c4->q8] with generating sets:
      [ (1,2,3,4)(5,8,7,6) ]
      [ (1,2,3,4)(5,8,7,6), (1,5,3,7)(2,6,4,8) ]
    :  Range = Crossed module [c4->q8] with generating sets:
      [ (1,2,3,4)(5,8,7,6) ]
      [ (1,2,3,4)(5,8,7,6), (1,5,3,7)(2,6,4,8) ] 
    : Source Homomorphism maps source generators to:
      [ ( 1,4,3,2)(5,6,7,8) ]
    : Range Homomorphism maps range generators to:
      [ ( 1,4,3,2)(5,6,7,8), (1,7,3,5)(2,8,4,6) ]
      isXModMorphism? true