ComplementConjugatingAgWord( N, U, V )
ComplementConjugatingAgWord( N, U, V, K )
Let N, U, V and K be ag groups with a common parent group G, such that N is p-elementary abelian and normal in G, <U>*<N> = <V>*<N>, <U> cap <N> = <V> cap <N> = {1}, K is a normal subgroup of <U> <N> contained in <U> cap <V> and U is conjugate to V under an element n of N. Then this function returns an element n of N such that <U>^n = <V> as ag word. If K is not given, the trivial subgroup is assumed.
In a typical application N is a normal p-elementary abelian subgroup and U, V and K are subgroups such that U/K is a q-group with qneq p.
Note that this function does not check any of the above conditions. So
the result may either be false or an ag word with does not conjugate
U into V, if U and V are not conjugate.
gap> c3a := Subgroup( s4, [ b ] );
Subgroup( s4, [ b ] )
gap> c3b := Subgroup( s4, [ b*c ] );
Subgroup( s4, [ b*c ] )
gap> v4 := Subgroup( s4, [ c, d ] );
Subgroup( s4, [ c, d ] )
gap> ComplementConjugatingAgWord( v4, c3a, c3b );
d
gap> c3a ^ d;
Subgroup( s4, [ b*c ] )
GAP 3.4.4