> < ^ Date: Wed, 05 Nov 1997 12:59:13 +0000 (GMT)
> < ^ From: Alexander Hulpke <hulpke@math.colostate.edu >
< ^ Subject: Re: Normalizer

Dear Gap-Forum,

Bruce Coletti asked:

What GAP3.4.4 function returns the normalizer in a group G of an arbitrary
*subset* (not *subgroup*) X of G? Thanks.

The normalizer of a set is the set-wise stabilizer. Thus:

gap> s:=Set([(1,2),(3,4)]);
[ (3,4), (1,2) ]
gap> n:=Stabilizer(g,s,OnSets);
Subgroup( Group( (1,2,3,4), (1,2) ), [ (1,2), (1,3)(2,4) ] )

Note that GAP uses by standard the ^ operator to act. Thus 'OnSets' acts on
the set elements via ^ which is the conjugation action on the group we want.

This stabilizer calculation performs a simple orbit/stabilizer algorithm.
Therefore if the normalizer you want is of index more than a few hundred,
you may find it a little bit slow.
If this is the case and you need improvements, please write us again, as
there are some improvements possible.

Hope that helps,


> < [top]