On the upper central series of infinite groups
- Autores: Maria De Falco, F. de Giovanni, Carmela Musella, Yaroslav P. Sysak
- Localización: Proceedings of the American Mathematical Society, ISSN 0002-9939, Vol. 139, Nº 2, 2011, págs. 385-389
- Idioma: inglés
- DOI: 10.1090/s0002-9939-2010-10625-1
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Resumen
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 is any group, the hypercentre factor group is finite if and only if contains a finite normal subgroup such that is hypercentral (where the hypercentre of is defined as the last term of its upper central series).
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