18.113 (2014)

Let $\mathcal{M}$ be a finite set of finite simple nonabelian groups. Is it true that a periodic group saturated with groups from $\mathcal{M}$ (see 14.101) is isomorphic to one of groups in $\mathcal{M}$? The case where $\mathcal{M}$ is one-element is of special interest.