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On primitive overgroups of quasiprimitive permutation groups

โœ Scribed by Robert W. Baddeley; Cheryl E. Praeger

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
428 KB
Volume
263
Category
Article
ISSN
0021-8693

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โœฆ Synopsis

A permutation group is said to be quasiprimitive if all its non-trivial normal subgroups are transitive. We investigate pairs (G, H ) of permutation groups of degree n such that G H S n with G quasiprimitive and H primitive. An explicit classification of such pairs is obtained except in the cases where the primitive group H is either almost simple or the blow-up of an almost simple group. The theory in these remaining cases is investigated in separate papers. The results depend on the finite simple group classification.

๐Ÿ“œ SIMILAR VOLUMES

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This paper precisely classifies all simple groups with subgroups of index n and all primitive permutation groups of degree n, where n = 2.3', 5.3' or 10.3' for Y 2 1. As an application, it proves positively Gardiner and Praeger's conjecture in [6] regarding transitive groups with bounded movement.