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Computing sylow subgroups of permutation groups using homomorphic images of centralizers

โœ Scribed by Gregory Butler; John Cannon

Publisher
Elsevier Science
Year
1991
Tongue
English
Weight
784 KB
Volume
12
Category
Article
ISSN
0747-7171

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โœฆ Synopsis

The ability to construct the Sylow subgroups of a large finite permutation group is fundamental to a number of important algorithms for analysing the structure of such a group. In this paper we describe an algorithm which constructs a Sylow subgroup by restricting the problem to images of centralizers under the natural homomorphisms given by actions on invariant sets and partitions of points. The algorithm is essentially as efficient as that used for computing centralizers in permutation groups.

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## dedicated to john cossey on the occasion of his 60th birthday An extension of the well-known Frobenius criterion of p-nilpotence in groups with modular Sylow p-subgroups is proved in the paper. This result is useful to get information about the classes of groups in which every subnormal subgrou