J Austral Math Soc Ser A 59 pp384--398, 1995.

Groups with all Subgroups Normal-By-Finite

J. T. Buckley, John C. Lennox, B. H. Neumann, Howard Smith and James Wiegold

Abstract

A group G has all of its subgroups normal-by-finite if H / core_G(H) is finite for all subgroups H of G. These groups can be quite complicated in general, as is seen from the so-called Tarski groups. However, the locally finite groups of this type are shown to be abelian-by-finite; and they are then boundedly core-finite, that is to say, there is a bound depending in G only for the indices |H : core_G(H)|.

1991 AMS Subject Classification: 20F24, 20F30

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Authors

J. T. Buckley

Department of Mathematics, University of Western Michigan, Kalamazoo, MI, USA.

John C. Lennox

School of Mathematics, University of Wales College of Cardiff, Cardiff, UK.

B. H. Neumann

School of Mathematical Sciences, Australian National University, Canberra, ACT, Australia.

Howard Smith

Department of Mathematics, Bucknell University, Lewisburg, PA, USA.

James Wiegold

School of Mathematics, University of Wales College of Cardiff, Cardiff, UK.