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Zbl 0642.20019
Kantor, W.M.; Taylor, D.E.
Polynomial-time versions of Sylow's theorem. (English)
[J] J. Algorithms 9, No.1, 1-17 (1988). ISSN 0196-6774

Imposing certain restrictions on the composition factors the authors present polynomial time algorithms for solving the following problems for permutation groups $G\le S\sb n:$ (1) given Sylow p-subgroups $P\sb 1$ and $P\sb 2$ of G, find $g\in G$ conjugating $P\sb 1$ to $P\sb 2$; (2) find a Sylow p-subgroup of G; (3) given a p-subgroup K of G, find a Sylow p-subgroup of G containing K; (4) given $N\triangleleft G$ with $(\vert N\vert,\vert G/N\vert)=1$ and complements $H\sb 1$ and $H\sb 2$ to N, find $g\in G$ conjugating $H\sb 1$ to $H\sb 2$; (5) given $N\triangleleft G$ with $(\vert N\vert,\vert G/N\vert)=1$, find a complement to N in G. If G is solvable, the analogues of (1), (2), and (3) for $\pi$-subgroups are solved as well. \par Polynomial time algorithms for these problems in arbitrary permutation groups can be found in a later paper of {\it W. M. Cantor} [J. Comput. Syst. Sci. 30, 359-394 (1985; Zbl 0573.20022)], however that version uses the classification of finite simple groups.
[P.P.Pálfy]

MSC 2000:: *20D20 Sylow subgroups of finite groups
20-04 Machine computation, programs (group theory)
68Q25 Analysis of algorithms and problem complexity
20B35 Subgroups of symmetric groups

Keywords: polynomial time algorithms; permutation groups; Sylow p-subgroups; complements; $\pi $-subgroups

Citations: Zbl 0573.20022

Cited in: Zbl 0708.20001

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