Abstract
In this paper we extend some classical theorems involving the terms and the factors groups of the central series of a group. Specifically we show that a periodic hypercentral-by-Chernikov group is Chernikov-by-hypercentral and obtain explicit bounds that describe numerical invariants of the second structure of the group as function of the first one.
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Supported by Proyecto MTM2010-19938-C03-03 of the Department of I+D+i of MINECO (Spain), the Department of I+D of the Government of Aragón (Spain) and FEDER funds from European Union.
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Kurdachenko, L.A., Otal, J. Groups with Chernikov factor-group by hypercentral. RACSAM 109, 569–579 (2015). https://doi.org/10.1007/s13398-014-0201-7
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DOI: https://doi.org/10.1007/s13398-014-0201-7
Keywords
- Upper central series of a group
- Hypercenter of a group
- Hypercentral group
- Locally nilpotent residual of a group
- \(p\)-rank of an abelian group
- \(p\)-minimax and minimax rank of a group
- Chernikov group
- Schur’s theorem
- Baer’s theorem
- \(Z\)-decomposition
- \(RG\)-hypercentral module
- \(RG\)-nilpotent module