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
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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).