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Zbl 0731.20005
Kantor, William M.
Finding Sylow normalizers in polynomial time. (English)
[J] J. Algorithms 11, No.4, 523-563 (1990). ISSN 0196-6774

Let G be a subgroup of $S\sb n$, 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 $N\sb G(P)$ 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 $\pi$-subgroups for a set of primes $\pi$.
[I.Janiszczak (Essen)]

MSC 2000:: *20B40 Computational methods (permutation groups)
20D20 Sylow subgroups of finite groups
20B35 Subgroups of symmetric groups
68Q25 Analysis of algorithms and problem complexity

Keywords: symmetric group; polynomial-time algorithms; Sylow p-subgroups; normalizer; simple factors; Hall $\pi$-subgroups

Cited in: Zbl 0884.20002 Zbl 0804.53056

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