(2,3)-generation of the special linear groups of dimensions 9, 10 and 11

TL;DR

This paper proves that the special linear groups PSL_n(q) for n=9, 10, 11 are generated by two elements of orders 2 and 3, providing explicit generators for these groups across all q.

Contribution

It establishes (2,3)-generation for PSL_n(q) with explicit generators for n=9, 10, 11, extending known results to these specific dimensions.

Findings

PSL_9(q), PSL_10(q), PSL_11(q) are (2,3)-generated for all q

Explicit generators of orders 2 and 3 are constructed for SL_n(q)

The results hold universally for all q in these dimensions

Abstract

We prove that the groups PSL_n(q) are (2,3)-generated for n=9,10 or 11 and all q. Actually, we find out explicit generators x_n and y_n of respective orders 2 and 3, for the groups SL_n(q).