9.27 (1984)

Let $M$ be a subgroup of a finite group $G$, $A$ an abelian 2-subgroup of $M$, and suppose that $A^g$ is not contained in $M$ for some $g$ from $G$. Determine the structure of $G$ under the hypothesis that $\langle A, A^x \rangle = G$ whenever the subgroup $A^x, x \in G$, is not contained in $M$.