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Finding Sylow normalizers in polynomial time. (English) Zbl 0731.20005
Let G be a subgroup of S n , the symmetric group on n points. In continuation of his previous articles on polynomial-time algorithms for finding Sylow p-subgroups of G the author shows in the present paper that there exists also a polynomial-time algorithm for given prime p which finds the normalizer N G (P) of a Sylow p-subgroup P of G. This is done by polynomial-time reducing the problem to an algorithm called SIMPLENORMALIZER. It deals with simple factors of G, also in polynomial time. In particular, in the case where G is solvable the author generalizes this result to Hall π-subgroups for a set of primes π.

MSC:
20B40Computational methods (permutation groups)
20D20Sylow subgroups of finite groups, Sylow properties, π-groups, π-structure
20B35Subgroups of symmetric groups
68Q25Analysis of algorithms and problem complexity