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Bounds on finite quasiprimitive permutation groups

Part of: Permutation groups

Published online by Cambridge University Press:  09 April 2009

Cheryl E. Praeger  and
Aner Shalev
Cheryl E. Praeger
Affiliation:
Department of Mathematics and Statistics, University of Western Australia, 35 Stirling Highway, Crawley WA 6009, Australia e-mail: [email protected].
Aner Shalev
Affiliation:
Institute of Mathematics, Hebrew University, Jerusalem 91904, Israel e-mail: [email protected]
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Abstract

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A permutation group is said to be quasiprimitive if every nontrivial normal subgroup is transitive. Every primitive permutation group is quasiprimitive, but the converse is not true. In this paper we start a project whose goal is to check which of the classical results on finite primitive permutation groups also holds for quasiprimitive ones (possibly with some modifications). The main topics addressed here are bounds on order, minimum degree and base size, as well as groups containing special p-elements. We also pose some problems for further research.

Keywords

primitive permutation groupquasiprimitive permutation group.

MSC classification

Secondary: 20B05: General theory for finite groups 20B15: Primitive groups 20B35: Subgroups of symmetric groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 71 , Issue 2 , October 2001 , pp. 243 - 258
Copyright
Copyright © Australian Mathematical Society 2001

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