Normalizer( S, U )
Let S and U be groups with a common parent group G. Then
Normalizer
returns the normalizer of U in S.
The normalizer N_{<S>}( <U> ) of U in S is the biggest subgroup of S which leaves U invariant under conjugation.
If S is the parent group of U then Normalizer
sets and tests
U.normalizer
.
gap> s4 := Group( (1,2,3,4), (1,2) ); Group( (1,2,3,4), (1,2) ) gap> c2 := Subgroup( s4, [ (1,2) ] ); Subgroup( Group( (1,2,3,4), (1,2) ), [ (1,2) ] ) gap> Normalizer( s4, c2 ); Subgroup( Group( (1,2,3,4), (1,2) ), [ (3,4), (1,2) ] )
The default function GroupOps.Normalizer
uses Stabilizer
(see
Stabilizer) in order to compute the stabilizer of U in S acting by
conjugation (see ConjugateSubgroup).
GAP 3.4.4