Primitive permutation groups containing a cycle

Authors

  • G. A. Jones University of Southampton

Keywords:

primitive group, cycle, fixed points, alternating group

Abstract

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. 10.1017/S000497271300049X

Author Biography

G. A. Jones, University of Southampton

Mathematics, Emeritus Professor

Published

2013-12-02

Issue

Vol. 89 No. 1 (2014)

Section

Articles
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