On the upper central series of infinite groups
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- by M. De Falco, F. de Giovanni, C. Musella and Y. P. Sysak PDF
- Proc. Amer. Math. Soc. 139 (2011), 385-389 Request permission
Abstract:
Two relevant theorems by R. Baer and P. Hall show that a group is finite over a term with finite ordinal type of its upper central series if and only if it is finite-by-nilpotent. Extending these results, we prove here that if $G$ is any group, the hypercentre factor group $G/\bar Z(G)$ is finite if and only if $G$ contains a finite normal subgroup $N$ such that $G/N$ is hypercentral (where the hypercentre $\bar Z(G)$ of $G$ is defined as the last term of its upper central series).References
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Additional Information
- M. De Falco
- Affiliation: Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Complesso Universitario Monte S. Angelo, Via Cintia, I-80126 Napoli, Italy
- Email: mdefalco@unina.it
- F. de Giovanni
- Affiliation: Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Complesso Universitario Monte S. Angelo, Via Cintia, I-80126 Napoli, Italy
- Email: degiovan@unina.it
- C. Musella
- Affiliation: Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Complesso Universitario Monte S. Angelo, Via Cintia, I-80126 Napoli, Italy
- Email: cmusella@unina.it
- Y. P. Sysak
- Affiliation: Institute of Mathematics, Ukrainian National Academy of Sciences, vul. Tereshchenkivska 3, 01601 Kiev, Ukraine
- Email: sysak@imath.kiev.ua
- Received by editor(s): November 6, 2009
- Published electronically: September 27, 2010
- Communicated by: Jonathan I. Hall
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 385-389
- MSC (2010): Primary 20E15
- DOI: https://doi.org/10.1090/S0002-9939-2010-10625-1
- MathSciNet review: 2736322
Dedicated: To Bernhard Amberg on his 70th birthday