70.9 CorrespondingAutomorphism

CorrespondingAutomorphism( G, w )

If G is a polycyclically presented group of automorphisms of a group P as returned by AgNormalizedAutomorphisms (see AgNormalizedAutomorphisms) or AgNormalizedOuterAutomorphisms (see AgNormalizedOuterAutomorphisms), and w is an element of G then the automorphism of P corresponding to w is returned.

    gap> g:= TwoGroup( 64, 173 );;
    gap> g.name := "G173";;
    gap> autg := AgNormalizedAutomorphisms ( g );
    Group( g0, g1, g2, g3, g4, g5, g6, g7, g8 )
    gap> CorrespondingAutomorphism ( autg, autg.2*autg.1^2 );
    GroupHomomorphismByImages( G173, G173, [ a1, a2, a3, a4, a5, a6 ],
    [ a1, a2*a4, a3*a6, a4*a6, a5, a6 ] ) 

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