7.111 InnerAutomorphism

InnerAutomorphism( G, g )

InnerAutomorphism returns the automorphism on the group G that takes each element h to h ^ g. g must be an element in the parent group of G (but need not actually be in G) that normalizes G.

    gap> s5 := Group( (1,2), (1,2,3,4,5) );;  s5.name := "s5";;
    gap> i := InnerAutomorphism( s5, (1,2) );
    InnerAutomorphism( s5, (1,2) )
    gap> (1,2,3,4,5) ^ i;
    (1,3,4,5,2) 

InnerAutomorphism( G, g ) calls ConjugationGroupHomomorphism( G, G, g ) (see ConjugationGroupHomomorphism).

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