Two-closure of odd permutation group in polynomial time Original Research Article

The k-closure G(k) of a permutation group G on a finite set V is by definition the largest permutation group on V having the same orbits on Vk as G. We prove that if the order of G is odd, then a set of generators of G(2) can be found in polynomial time in the cardinality of V. If in addition G is primitive, then given k⩾1 we can list all elements of G(k) within the same time.