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The primitive permutation groups of certain degrees

โœ Scribed by Cai Heng Li


Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
764 KB
Volume
115
Category
Article
ISSN
0022-4049

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โœฆ Synopsis


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.


๐Ÿ“œ SIMILAR VOLUMES


On the Minimal Degree of a Primitive Per
โœ Robert Guralnick; Kay Magaard ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 237 KB

We improve a result of Liebeck and Saxl concerning the minimal degree of a primitive permutation group and use it to strengthen a result of Guralnick and Neubauer on generic covers of Riemann surfaces.

The affine primitive permutation groups
โœ Colva M. Roney-Dougal; William R. Unger ๐Ÿ“‚ Article ๐Ÿ“… 2003 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 189 KB

In this paper we complete the classification of the primitive permutation groups of degree less than 1000 by determining the irreducible subgroups of GL(n, p) for p prime and p n < 1000. We also enumerate the maximal subgroups of GL(8, 2), GL(4, 5) and GL(6, 3).

On the List of Finite Primitive Permutat
โœ FRANCIS BUEKENHOUT; DIMITRI LEEMANS ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 454 KB

We complete data in Sims' list of the 406 primitive permutation groups of degree โ‰ค 50, as given in a CAYLEY library, by an explicit description of the structure of the 202 groups missing till now. The completed list is available in MAGMA.

Transitive Subgroups of Primitive Permut
โœ Martin W. Liebeck; Cheryl E. Praeger; Jan Saxl ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 492 KB

to helmut wielandt on the occasion of his 90th birthday We investigate the finite primitive permutation groups G which have a transitive subgroup containing no nontrivial subnormal subgroup of G. The conclusion is that such primitive groups are rather rare, and that their existence is intimately co

On primitive overgroups of quasiprimitiv
โœ Robert W. Baddeley; Cheryl E. Praeger ๐Ÿ“‚ Article ๐Ÿ“… 2003 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 428 KB

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 wh