Martina Capasso

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math.GR2026

New variations on the theme of Baer's theorem

Martina Capasso, Liliana Lancellotti, Pavel Shumyatsky

Let $γ_{s} (G)$ and $Z_{s} (G)$ denote the $s$ -th terms of the lower and upper central series of a group $G$ , respectively. A classical theorem by R. Baer states that if $Z_{s} (G)$ has fin…

math.GR2025

On Chernikov-by-nilpotent groups

Martina Capasso, Liliana Lancellotti, Pavel Shumyatsky

Let $γ_{k} = [x_{1}, \dots, x_{k}]$ be the $k$ -th lower central group-word. Given a group $G$ , we write $X_{k} (G)$ for the set of $γ_{k}$ -values and $γ_{k} (G)$ for the $k$ -th term of the lower cen…