The $(2,3)$-generation of the finite simple orthogonal groups, I

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

Published 2023-06-04Version 1

The complete classification of the finite simple groups that are $(2,3)$-generated is a problem which is still open only for orthogonal groups. Here, we construct $(2, 3)$-generators for the finite odd-dimensional orthogonal groups $\Omega_{2k+1}(q)$ with $q$ odd and $k\geq 4$. As a byproduct we also obtain $(2,3)$-generators for $\Omega_{4k}^+(q)$ with $k\geq 3$ and $q$ odd, and for $\Omega_{4k+2}^\pm(q)$ with $k\geq 4$ and $q\equiv \pm 1 \pmod 4$.