On some subgroups of linear groups over $\mathbb{F}_2$ generated by elements of order $3$

TL;DR

This paper studies specific subgroups of linear groups over the field with two elements, generated by elements of order 3 with particular commutator properties, contributing to understanding their structure.

Contribution

It characterizes subgroups of $GL(V)$ generated by conjugacy classes of order 3 elements with 2-dimensional commutator spaces over $ ext{GF}(2)$.

Findings

Identification of conditions for subgroup generation by order 3 elements

Structural insights into subgroups with specified commutator dimensions

Advancement in classification of linear groups over $ ext{GF}(2)$

Abstract

Let $V$ be a vector space over the field of order $2$. We investigate subgroups of the linear group $GL(V)$ which are generated by a conjugacy class $D$ of elements of order $3$ such that all $d$ in $D$ have $2$-dimensional commutator space $[V,d]$.