Author

P. Shumyatsky

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Preprint Sep 2026

Involutory automorphisms of finite groups of odd order

For a finite group $G$ we write $\gamma_\infty(G)$ 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 $\varphi$ such that $G=[G,\varphi]$ and suppose tha...

P. Shumyatsky, Gabriel Santa Catarina de Souza · 0 citations

Preprint Sep 2026

Rank properties of commutators in finite groups

For a subset $S$ of a finite group $G$, let $I_G(S)$ denote the set of commutators $[g,x]=g^{-1}g^x$, where $g\in G$ and $x\in S$. Suppose that a finite group $G$ has a Carter subgroup $C$, that is, a nilpotent subgroup containing its normalizer. Suppose that any subgroup generated by a subset of $I_G(C)$ is $r$-genera...

Cristina Acciarri, R. Guralnick, Evgeny Khukhro et al. · 0 citations