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Transitive simple subgroups of wreath products in product action

Part of: Permutation groups

Published online by Cambridge University Press:  09 April 2009

Robert W. Baddeley ,
Cheryl E. Praeger  and
Csaba Schneider
Robert W. Baddeley
Affiliation:
32 Arbury Road, Cambridge CB4 2JE, UK e-mail: robert.baddeley@ntlworld.com
Cheryl E. Praeger
Affiliation:
School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley 6009 WA, Australia e-mail: praeger@maths.uwa.edu.au URL: http://www.maths.uwa.edu.au/~praeger
Csaba Schneider
Affiliation:
Informatics Laboratory, Computer and Automation Research Institute, The Hungarian Academy of Sciences, 1111. Budapest, Lágymányosi u. 11Hungary e-mail: csaba.schneider@sztaki.hu URL: www.sztaki.hu/~schneider
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Abstract

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A transitive simple subgroup of a finite symmetric group is very rarely contained in a full wreath product in product action. All such simple permutation groups are determined in this paper. This remarkable conclusion is reached after a definition and detailed examination of ‘Cartesian decompositions’ of the permuted set, relating them to certain ‘Cartesian systems of subgroups’. These concepts, and the bijective connections between them, are explored in greater generality, with specific future applications in mind.

Keywords

permutation groupswreath productsproduct actioninnately transitive groupsplinthCartesian decompositionsCartesian systemsfinite simple groups

MSC classification

Secondary: 20B05: General theory for finite groups 20B15: Primitive groups 20B35: Subgroups of symmetric groups 20B99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 77 , Issue 1 , August 2004 , pp. 55 - 72
Copyright
Copyright © Australian Mathematical Society 2004

References

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