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Groups with many permutable subgroups

Part of: Special aspects of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

Mario Curzio ,
John Lennox ,
Akbar Rhemtulla  and
James Wiegold
Mario Curzio
Affiliation:
Dipartimento di Matematica Pura e Applicata Università Degli Studi di NapoliNapoli, Italia
John Lennox
Affiliation:
School of Mathematics University of WalesCollege of Cardiff Cardiff CF2 4AG Wales
Akbar Rhemtulla
Affiliation:
Department of Mathematics University of AlbertaEdmonton, Alberta, Canada
James Wiegold
Affiliation:
School of Mathematics University of WalesCollege of Cardiff Cardiff CF2 4AG Wales
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Abstract

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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.

MSC classification

Secondary: 20F16: Solvable groups, supersolvable groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 48 , Issue 3 , June 1990 , pp. 397 - 401
Copyright
Copyright © Australian Mathematical Society 1990

References

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