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,