Year: 2026
Type: preprint
Abstract: For a finite group $G$ we write $γ_\infty(G)$ to denote the nilpotent residual of $G$, that is, the intersection of all terms of the lower central series. The following theorem is proved: Let $G$ be a finite group of odd order admitting an involutory automorphism $φ$ such that $G=[G,φ]$ and suppose that $γ_\infty(C_G(φ))$ has order $m$. Then the order of $γ_\infty(G')$ is bounded by a function depending only on $m$. This complements several earlier results on groups of odd order admitting involutory automorphisms.
Source: arXiv (Cornell University)
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: W7212125003