14.101 (1999)

A group $G$ is saturated with groups from a class $\mathfrak{X}$ if every finite subgroup $K \leqslant G$ is contained in a subgroup $L \leqslant G$ isomorphic to some group from $\mathfrak{X}$. Is it true that a periodic group saturated with finite simple groups of Lie type of uniformly bounded ranks is itself a simple group of Lie type of finite rank?