8.40 (1982)

Describe the finite groups generated by a conjugacy class $D$ of involutions which satisfies the following property: if $a, b \in D$ and $|ab| = 4$, then $[a, b] \in D$. This condition is satisfied, for example, in the case where $D$ is a conjugacy class of involutions of a known finite simple group such that $\langle C_D(a) \rangle$ is a 2-group for every $a \in D$.