The $(2,3)$-generation of the finite special unitary groups of dimension $n\geq 9$

M. A. Pellegrini, M. C. Tamburini Bellani

Published 2018-07-24Version 1

In this paper we prove that the unitary groups $SU_n(q^2)$ and $PSU_n(q^2)$ are $(2,3)$-generated for any prime power $q$ and any integer $n\geq 9$. By previous results this implies that, if $n\geq 3$ and $n\neq 8$, the groups $SU_n(q^2)$ and $PSU_n(q^2)$ are $(2,3)$-generated, except when $(n,q)\in\{(3,2),(3,3),(3,5),(4,2), (4,3),(5,2)\}$.