Products of conjugate permutations

Manfred Droste and Rüdiger Göbel

Vol. 94 (1981), No. 1, 47–60

DOI: 10.2140/pjm.1981.94.47

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