[GAP Forum] Set stabilizer

[Alastair Donaldson]

Dear Forum

Given a group G acting on {1,...,n} and a subset X of {1,...n}, I understand that the algorithm which GAP uses to compute the set-wise stabilizer of X in G is not a polynomial time algorithm (even though it is often quite efficient).

However, if I have a subgroup H of G, is it possible to answer the question "is H the set stabilizer of X in G?" in polynomial time?

For my specific application it is always the case that H is a subgroup of the set stabilizer, and I want to know if it is actually the whole thing.

Thanks, in advance

Alastair Donaldson