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PRIMITIVE PERMUTATION GROUPS CONTAINING A CYCLE

Part of: History of mathematics and mathematicians Permutation groups Group theory and generalizations

Published online by Cambridge University Press:  18 July 2013

GARETH A. JONES
GARETH A. JONES*
Affiliation:
School of Mathematics, University of Southampton, Southampton SO17 1BJ, UK email G.A.Jones@maths.soton.ac.uk
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Abstract

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The primitive finite permutation groups containing a cycle are classified. Of these, only the alternating and symmetric groups contain a cycle fixing at least three points. This removes a primality condition from a classical theorem of Jordan. Some applications to monodromy groups are given, and the contributions of Jordan and Marggraff to this topic are briefly discussed.

Keywords

primitive groupcyclefixed pointsalternating group

MSC classification

Secondary: 20B15: Primitive groups 01A55: 19th century 20-03: Historical (must also be assigned at least one classification number from Section 01) 20B20: Multiply transitive finite groups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 89 , Issue 1 , February 2014 , pp. 159 - 165
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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