J Austral Math Soc Ser A 48 pp397--401, 1990.

Groups with Many Permutable Solutions

Mario Curzio, John Lennox, Akbar Rhemtulla and James Wiegold

(Received 6 December 1988; revised 1 August 1989)

Abstract

We consider the influence on a group G of the condition that every infinite set of cyclic subgroups of G contains a pair that permute and prove (Theorem 1) that finitely generated soluble groups with this condition are centre-by-finite, and (Theorem 2) that torsion free groups satisfying the condition are abelian.

1980 AMS Subject Classification (1985 Revision): 20F16

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Authors

Mario Curzio: Dipartimento di Matematica, Pura e Applicata, Università Degli Studi di Napoli, Napoli, Italia.
John Lennox: School of Mathematics, University of Wales, College of Cardiff, Cardiff CF2 4AG, Wales.
Akbar Rhemtulla: Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada.
James Wiegold: School of Mathematics, University of Wales, College of Cardiff, Cardiff CF2 4AG, Wales.

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