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PRIMITIVE PERMUTATION GROUPS CONTAINING A CYCLE

Published online by Cambridge University Press:  18 July 2013

GARETH A. JONES*
Affiliation:
School of Mathematics, University of Southampton, Southampton SO17 1BJ, UK email [email protected]
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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.

Type
Research Article
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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