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Journal of Group Theory

Editor-in-Chief: Parker, Christopher W.

Managing Editor: Wilson, John S. / Khukhro, Evgenii I. / Kramer, Linus

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Volume 12, Issue 4


Finiteness conditions on characteristic closures and cores of subgroups

Giovanni Cutolo
  • Università degli Studi di Napoli “Federico II”, Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Via Cintia, Monte S. Angelo, 80126 Napoli, Italy. E-mail: , Url: http://www.dma.unina.it/~cutolo/
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/ Howard Smith
  • Howard Smith, Department of Mathematics, Bucknell University, Lewisburg, Pennsylvania 17837, U.S.A. E-mail:
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/ James Wiegold
Published Online: 2008-10-20 | DOI: https://doi.org/10.1515/JGT.2008.092


We characterize groups in which every abelian subgroup has finite index in its characteristic closure. In a group with this property every subgroup H has finite index in its characteristic closure and there is an upper bound for this index over all subgroups H of G. For every prime p we construct groups G with this property that are infinite nilpotent p-groups of class 2 and exponent p 2 in which G′ = Z(G) is finite and Aut G acts trivially on G/G′.

We also characterize abelian groups with the dual property that every subgroup has finite index over its characteristic core.

About the article

Received: 2007-10-31

Revised: 2008-06-06

Published Online: 2008-10-20

Published in Print: 2009-07-01

Citation Information: Journal of Group Theory, Volume 12, Issue 4, Pages 591–610, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: https://doi.org/10.1515/JGT.2008.092.

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