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LOCALLY FINITE GROUPS ALL OF WHOSE SUBGROUPS ARE BOUNDEDLY FINITE OVER THEIR CORES

Published online by Cambridge University Press:  01 September 1997

G. CUTOLO ,
E. I. KHUKHRO ,
J. C. LENNOX ,
S. RINAURO ,
H. SMITH  and
JAMES WIEGOLD
G. CUTOLO
Affiliation:
Università degli Studi di Napoli ‘Federico II’, Dipartimento di Matematica e Applicazioni, Via Cintia–Monte S. Angelo, I-80126 Napoli, Italy
E. I. KHUKHRO
Affiliation:
School of Mathematics, University of Wales College of Cardiff, 23 Senghennydd Road, P.O. Box No. 926, Cardiff CF2 4YH
J. C. LENNOX
Affiliation:
School of Mathematics, University of Wales College of Cardiff, 23 Senghennydd Road, P.O. Box No. 926, Cardiff CF2 4YH
S. RINAURO
Affiliation:
Università degli Studi della Basilicata, Dipartimento di Matematica, Via N. Sauro, 85, I-85100 Potenza, Italy
H. SMITH
Affiliation:
Department of Mathematics, Bucknell University, Lewisburg, PA 17837, USA
JAMES WIEGOLD
Affiliation:
School of Mathematics, University of Wales College of Cardiff, 23 Senghennydd Road, P.O. Box No. 926, Cardiff CF2 4YH
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Abstract

For n a positive integer, a group G is called core-n if H/HG has order at most n for every subgroup H of G (where HG is the normal core of H, the largest normal subgroup of G contained in H). It is proved that a locally finite core-n group G has an abelian subgroup whose index in G is bounded in terms of n.

Type
Research Article
Information
Bulletin of the London Mathematical Society , Volume 29 , Issue 5 , September 1997 , pp. 563 - 570
Copyright
© The London Mathematical Society 1997

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