Let gamma_i(G) and Z_i(G) denote the i-th terms of the lower and upper central series of a group G, respectively. P. Hall showed that if gamma_{i+1}(G) is finite then the index |G:Z_{2i}(G)| is finite. We- prove that the same result holds under the weaker hypothesis that |gamma_{i+1}(G):(gamma_{i+1}(G)cap Z_i(G)| is finite.
Generalizing a theorem of P. Hall on finite-by-nilpotent groups / G. Fernández-Alcober; M. Morigi. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - STAMPA. - 137:(2009), pp. 425-429. [10.1090/S0002-9939-08-09688-3]
Generalizing a theorem of P. Hall on finite-by-nilpotent groups
MORIGI, MARTA
2009
Abstract
Let gamma_i(G) and Z_i(G) denote the i-th terms of the lower and upper central series of a group G, respectively. P. Hall showed that if gamma_{i+1}(G) is finite then the index |G:Z_{2i}(G)| is finite. We- prove that the same result holds under the weaker hypothesis that |gamma_{i+1}(G):(gamma_{i+1}(G)cap Z_i(G)| is finite.File in questo prodotto:
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