A note about the (2,3)-generation of SL_12(q)

TL;DR

This paper constructs explicit (2,3)-generators for the group SL_{12}(q) for all q except 2 and 4, using known subgroup classifications, simplifying the understanding of its generation properties.

Contribution

It provides a uniform, explicit construction of (2,3)-generators for SL_{12}(q) for most q, based solely on known subgroup structures, filling a gap in the literature.

Findings

Explicit (2,3)-generators for SL_{12}(q) for all q ≠ 2, 4

Simplified, traceable construction method

Based on known maximal subgroup classifications

Abstract

We provide explicit uniform type (2,3)-generators for the special linear group SL_{12}(q) for all q except for q=2 or 4. Our considerations are easily traceable, self-contained and based only on the known list of maximal subgroups of this group.