Generalizing a theorem of P. Hall on finite-by-nilpotent groups

Fernández-Alcober, Gustavo; Morigi, Marta

doi:10.1090/S0002-9939-08-09688-3

Generalizing a theorem of P. Hall on finite-by-nilpotent groups
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by Gustavo A. Fernández-Alcober and Marta Morigi PDF

Proc. Amer. Math. Soc. 137 (2009), 425-429 Request permission

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. In 1956 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.

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