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

Alcobér, Gustavo Fernandez; Morigi, Marta

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

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Let $γ_i(G)$ 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 $γ_{i+1}(G)$ is finite then the index $|G:Z_{2i}(G)|$ is finite. We prove that the same result holds under the weaker hypothesis that $|γ_{i+1}(G):γ_{i+1}(G)\cap Z_i(G)|$ is finite.