Uniform (2,k)-generation of the 4-dimensional classical groups

TL;DR

This paper investigates the conditions under which certain 4-dimensional classical groups can be generated by two elements, one of order 2 and the other of order k, expanding understanding of their algebraic structure.

Contribution

It provides new results on (2,k)-generation of SL(4,q), Sp(4,q), and SU(4,q^2), including cases where q is even and k=4, extending previous knowledge.

Findings

Established (2,k)-generation criteria for SL(4,q), Sp(4,q), SU(4,q^2)

Identified conditions for generation when q is even and k=4

Enhanced understanding of the algebraic structure of 4-dimensional classical groups

Abstract

In this paper we study the (2,k)-generation of the finite classical groups SL(4,q), Sp(4,q), SU(4,q^2) and their projective images. Here k is the order of an arbitrary element of SL(2,q), subject to the necessary condition k>= 3. When q is even we allow also k=4.