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Finite permutation groups with a transitive minimal normal subgroup

Published online by Cambridge University Press:  30 June 2004

John Bamberg  and
Cheryl E. Praeger
John Bamberg
Affiliation:
School of Mathematics and Statistics, University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia. E-mail: john.bam@maths.uwa.edu.au
Cheryl E. Praeger
Affiliation:
School of Mathematics and Statistics, University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia. E-mail: john.bam@maths.uwa.edu.au
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Abstract

A finite permutation group is said to be innately transitive if it contains a transitive minimal normal subgroup. In this paper, we give a characterisation and structure theorem for the finite innately transitive groups, as well as describing those innately transitive groups which preserve a product decomposition. The class of innately transitive groups contains all primitive and quasiprimitive groups.

Keywords

20B0520B15
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 89 , Issue 1 , July 2004 , pp. 71 - 103
Copyright
2004 London Mathematical Society

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Footnotes

The first author acknowledges the financial assistance of the Australian Postgraduate Award, UWA Winthrop Scholarship, and the Jean Rogerson Postgraduate Award.