On Chernikov-by-nilpotent groups

2025/11/29 by Martina Capasso, Capasso, Martina, Liliana Lancellotti +3
Mathematics · #Finite Group Theory Research #Limits and Structures in Graph Theory #Advanced Operator Algebra Research

paper · pdf · doi:10.48550/arxiv.2512.00615

Abstract

Let γ_k=[x₁,…,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 ⟨ g^X_k(G) ⟩ is a Chernikov group of size at most (m,n) for all g∈ G. The main result is that γ_k+1(G) is a Chernikov group and its size is (k,m,n)-bounded.

Citations

• BFC-theorems for higher commutator subgroups
• Groups with Boundedly Finite Conjugacy Classes of Commutators
• Average dimension of fixed point spaces with applications
• Groups Covered By Permutable Subsets

Related

• On finite-by-nilpotent groups
• Locally finite groups containing a 2-element with Chernikov centralizer
• A general Kirillov Theory for locally compact nilpotent groups
• On groups where the twisted conjugacy class of the unit element is a subgroup
• Baumslag-Solitar groups and residual nilpotence