R. I. Gvozdev, Ya. N. Nuzhin, “The minimal number of generating involutions whose product is $1$ for the groups $PSL_3(2^m)$ and $PSU_3(q^2)$”, Sibirsk. Mat. Zh., 2023, Volume 64, Number 6,Pages 1160

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The minimal number of generating involutions whose product is $1$ for the groups $PSL_3(2^m)$ and $PSU_3(q^2)$

R. I. Gvozdev, Ya. N. Nuzhin

Siberian Federal University, Krasnoyarsk

Abstract: Considering the groups $PSL_3(2^m)$ and $PSU_3(q^2)$, we find the minimal number of generating involutions whose product is $1$. This number is $7$ for $PSU_3(3^2)$ and $5$ or $6$ in the remaining cases.

Keywords: finite simple group, generating set of involutions, character of a group representation, special linear and unitary groups.

UDC: 512.542+512.547

MSC: 35R30

Received: 12.03.2023
Revised: 12.03.2023
Accepted: 25.09.2023

DOI: 10.33048/smzh.2023.64.605