The (2,3)-generation of the special unitary groups of dimension 6

TL;DR

This paper provides explicit (2,3)-generators for the special unitary groups SU_6(q^2) across all q, suggesting a uniform approach for all n≥6, advancing understanding of their generation properties.

Contribution

The paper introduces explicit (2,3)-generators for SU_6(q^2) for all q, proposing a uniform sequence applicable to all n≥6, which is a new construction in group theory.

Findings

Explicit (2,3)-generators for SU_6(q^2) for all q

Proposes a uniform sequence of generators for all n≥6

Advances understanding of generation properties of special unitary groups

Abstract

In this paper we give explicit (2,3)-generators of the unitary groups SU_6(q^ 2), for all q. They fit into a uniform sequence of likely (2,3)-generators for all n>= 6.