Generation of the group $SL_6(\mathbb{Z}+i\mathbb{Z})$ by three involutions

Rodion I. Gvozdev

Siberian Federal University, Krasnoyarsk, Russian Federation

Abstract: It is proved that the group $SL_6(\mathbb{Z}+i\mathbb{Z})$ is generated by three involutions. Previously, the solution of the problem on the existence of generating triples of involutions two of which commute was completed for the groups $SL_n(\mathbb{Z}+i\mathbb{Z})$ and $PSL_n(\mathbb{Z}+i\mathbb{Z})$ (Math. notes, 115 (2024), no. 3). The question of generating these groups by three involutions remained unresolved only for $SL_6(\mathbb{Z}+i\mathbb{Z})$.

Keywords: special linear group, the ring of Gaussian integers, generating triples of involutions.

UDC: 512.5

Received: 10.06.2024
Received in revised form: 15.07.2024
Accepted: 20.08.2024

Language: English