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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,

Alexander

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