Fast recognition of doubly transitive groups
Journal of Symbolic Computation - Special issue on computational group theory: part 2
On the computation of conjugacy classes in permutation groups
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
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Given a subgroup G= of S"n specified in terms of a generating set @C, when n@?10^6 we present algorithms to test the simplicity of G, to find all of its composition factors, and to find a composition series. While there are already existing algorithms for these purposes (due to Luks or Neumann) valid for all n, the ones in the present note are designed to replace many group theoretic computations by arithmetic calculations using properties of n and |G|.