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Groups with all subgroups normal-by-finite

Part of: Special aspects of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

J. T. Buckley ,
John C. Lennox ,
B. H. Neumann ,
Howard Smith  and
James Wiegold
J. T. Buckley
Affiliation:
Department of MathematicsUniversity of Western Michigan Kalamazoo, MI, USA
John C. Lennox
Affiliation:
School of MathematicsUniversity of Wales College of CardiffCardiff, UK
B. H. Neumann
Affiliation:
School of Mathematical Sciences Australian National University Canberra, ACT, Australia
Howard Smith
Affiliation:
Department of MathematicsBucknell University Lewisburg, PA, USA
James Wiegold
Affiliation:
School of MathematicsUniversity of Wales College of CardiffCardiff, UK
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Abstract

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A group G has all of its subgroups normal-by-finite if H / coreG(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 on G only for the indices | H: coreG(H)|.

MSC classification

Secondary: 20F24: FC-groups and their generalizations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 59 , Issue 3 , December 1995 , pp. 384 - 398
Copyright
Copyright © Australian Mathematical Society 1995

References

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