# 25.92 ComplementConjugatingAgWord

`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
April 1997