Vol. 94, No. 1, 1981

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ISSN: 0030-8730
Products of conjugate permutations

Manfred Droste and Rüdiger Göbel

Vol. 94 (1981), No. 1, 47–60
Abstract

Using combinatorial methods, we will prove the following theorem on the permutation group S0 of a countable set: If a permutation p S0 contains at least one infinite cycle then any permutation of S0 is a product of three permutations each conjugate to p. Similar results for permutations of uncoutable sets are shown and classical group theoretical results are derived from this.

Mathematical Subject Classification 2000
Primary: 20B07
Secondary: 04A20
Milestones
Received: 2 February 1979
Revised: 14 May 1980
Published: 1 May 1981
Authors
Manfred Droste
Rüdiger Göbel