This article is cited in 1 paper

Generating sets of conjugate involutions of groups $PSL_{n}(9)$

R. I. Gvozdev

Institute of Mathematics and Computer Science, Siberian Federal University, Krasnoyarsk

Abstract: G. Malle, J. Saxl, and T. Weigel in [Geom. Ded., 49, No. 1, 85—116 (1994)] formulated the following problem: For every finite simple non-Abelian group $G$, find the minimum number $n_c(G)$ of generators of conjugate involutions whose product equals 1. (See also Question 14.69c in [Unsolved Problems in Group Theory. The Kourovka Notebook, No. 20, E. I. Khukhro and V. D. Mazurov (eds.), Sobolev Institute of Mathematics SO RAN, Novosibirsk (2022); https://alglog.org/20tkt.pdf].) J. M. Ward [PhD Thesis, Queen Mary College, Univ. London (2009)] solved this problem for sporadic, alternating, and projective special linear groups $PSL_n(q)$ over a field of odd order $q$, except in the case $q=9$ for $n\geq4$ and also in the case $q\equiv3 ({\rm mod} 4)$ for $n=6$. Here we lift the restriction $q\neq9$ for dimensions $n\geq9$ and for the dimension $n=6$.

Keywords: skew-symmetric identity, finitely generated alternative algebra.

UDC: 512.54

Received: 16.01.2023
Revised: 19.07.2024

DOI: 10.33048/alglog.2023.62.403

 English version: Algebra and Logic, 2023, 62:4, 319–338