On transitive permutation groups with a subgroup satisfying a certain conjugacy condition-Reference-Cited by-同舟云学术

On transitive permutation groups with a subgroup satisfying a certain conjugacy condition

Published:1984-02 Issue:1 Volume:36 Page:69-86
ISSN:0263-6115
Container-title:Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
language:en
Short-container-title:J Aust Math Soc A

Author:

Praeger Cheryl E.

Abstract

AbstractLet G be transitive permutation group of degree n and let K be a nontrivial pronormal subgroup of G (that is, for all g in G, K and Kg are conjugate in (K, Kg)). It is shown that K can fix at most ½(n – 1) points. Moreover if K fixes exactly ½(n – 1) points then G is either An or Sn, or GL(d, 2) in its natural representation where n = 2d-1 ≥ 7. Connections with a result of Michael O'Nan are dicussed, and an application to the Sylow subgroups of a one point stabilizer is given.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics,Statistics and Probability

Reference21 articles.

1. On Primitive Permutation Groups with a Doubly Transitive Suborbit

2. Doubly transitive automorphism groups of block designs

3. Doubly transitive permutation groups which are not doubly primitive

4. Estimation of Sylow subgroups in primitive permutation groups

5. Normal Structure of the One-Point Stabilizer of a Doubly-Transitive Permutation Group. II

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