Bounds on finite quasiprimitive permutation groups

Cheryl E. Praeger; Aner Shalev

doi:10.1017/s1446788700002895

Bounds on finite quasiprimitive permutation groups

Cheryl E. Praeger^*, Aner Shalev

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	243-258
Number of pages	16
Journal	Journal of the Australian Mathematical Society
Volume	71
Issue number	2
DOIs	https://doi.org/10.1017/s1446788700002895
State	Published - Oct 2001

Bibliographical note

Funding Information:
This paper forms part of an Australian Research Council large grant project of the first author. The second author acknowledges the support of the Israel Science Foundation, founded by the Israeli Academy of Science and Humanities. © 2001 Australian Mathematical Society 0263-6115/2001 $A2.00 + 0.00

Keywords

Primitive permutation group
Quasiprimitive permutation group

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10.1017/s1446788700002895

Cite this

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AB - 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.

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Bounds on finite quasiprimitive permutation groups

Abstract

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Keywords

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