Year: 2025
Type: article
Abstract: In 1954, B. H. Neumann discovered that if $G$ is a group in which all conjugacy classes have finite cardinality at most $m$ , then the derived group $G'$ is finite of $m$ -bounded order. In 2018, G. Dierings and P. Shumyatsky showed that if $|x^G| \le m$ for any commutator $x\in G$ , then the second derived group $G''$ is finite and has $m$ -bounded order. This paper deals with finite groups in which $|x^G|\le m$ whenever $x\in G$ is a commutator of prime power order. The main result is that $G''$ has $m$ -bounded order.
Source: Glasgow Mathematical Journal
Authors: Débora Senise, Pavel Shumyatsky
Institution: Universidade de Brasília
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4413223628