7.33 (1980)

An elementary TI-subgroup $V$ of a finite group $G$ is said to be a subgroup of non-root type if $1 \neq N_V(V^g) \neq V$ for some $g \in G$. Describe the finite groups $G$ which contain a 2-subgroup $V$ of non-root type such that $[V, V^g] = 1$ implies that all involutions in $VV^g$ are conjugate to elements of $V$.