On Chernikov-by-nilpotent groups
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912738250326016 |
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| author | Capasso, Martina Lancellotti, Liliana Shumyatsky, Pavel |
| author_facet | Capasso, Martina Lancellotti, Liliana Shumyatsky, Pavel |
| contents | 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 central of $G$. This paper deals with groups in which $\langle g^{X_k(G)} \rangle$ is a Chernikov group of size at most $(m,n)$ for all $g\in G$. The main result is that $γ_{k+1}(G)$ is a Chernikov group and its size is $(k,m,n)$-bounded. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_00615 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Chernikov-by-nilpotent groups Capasso, Martina Lancellotti, Liliana Shumyatsky, Pavel Group Theory 20F24, 20E45 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 central of $G$. This paper deals with groups in which $\langle g^{X_k(G)} \rangle$ is a Chernikov group of size at most $(m,n)$ for all $g\in G$. The main result is that $γ_{k+1}(G)$ is a Chernikov group and its size is $(k,m,n)$-bounded. |
| title | On Chernikov-by-nilpotent groups |
| topic | Group Theory 20F24, 20E45 |
| url | https://arxiv.org/abs/2512.00615 |