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Some finiteness conditions concerning intersections of conjugates of subgroups

Published online by Cambridge University Press:  18 May 2009

John C. Lennox ,
Patrizia Longobardi ,
Mercede Maj ,
Howard Smith  and
James Wiegold
John C. Lennox
Affiliation:
School of Mathematics, University of Wales College of Cardiff, Cardiff CF2 4AG, Wales
Patrizia Longobardi
Affiliation:
Dipartimento di Matematica e Applicazioni, Università degli Studi Di Napoli, Monte S. Angelo—Via Cintia, 80126 Napoli, Italy
Mercede Maj
Affiliation:
Dipartimento di Matematica e Applicazioni, Università degli Studi Di Napoli, Monte S. Angelo—Via Cintia, 80126 Napoli, Italy
Howard Smith
Affiliation:
Department of Mathematics, Bucknell University, Lewisburg PA 17837, U.S.A.
James Wiegold
Affiliation:
School of Mathematics, University of Wales College of Cardiff, Cardiff CF2 4AG, Wales
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In [3], a group G was said to be a CF-group if, for every subgroup H of G, H/CoreGH is finite. It was shown there that a locally finite CF-group G is abelian-by-finite and that there is a bound for the indices |H: CoreGH| as H runs through all subgroups of G. (Groups for which such a bound exists were referred to in [3] as BCF-groups.) The CF-property was further investigated in [10], one of the main results there being that nilpotent CF-groups are (again) abelian-by-finite and BCF. In the present paper, we shall discuss the CF-property in conjunction with some related properties, which are defined as follows.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 37 , Issue 3 , September 1995 , pp. 327 - 335
Copyright
Copyright © Glasgow Mathematical Journal Trust 1995

References

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