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Let $V$ be a vector space over the field of order $2$. We investigatesubgroups 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 $2$-dimensionalcommutator space $[V,d]$.

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