Geodesic
Periodic groups saturated by finite simple groups~$U_3(2^m)$
Algebra i logika, Tome 47 (2008) no. 3, pp. 288-306.

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Let $\mathfrak M$ be a set of finite groups. A group $G$ is said to be saturated by the groups in $\mathfrak M$ if every finite subgroup of $G$ is contained in a subgroup isomorphic to a member of $\mathfrak M$. It is proved that a periodic group $G$ saturated by groups in a set $\{U_3(2^m)\mid m=1,2,\dots\}$ is isomorphic to $U_3(Q)$ for some locally finite field $Q$ of characteristic 2; in particular, $G$ is locally finite.
Keywords: periodic group, finite group, saturated group. 
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D. V. Lytkina; L. R. Tukhvatullina; K. A. Filippov. Periodic groups saturated by finite simple groups~$U_3(2^m)$. Algebra i logika, Tome 47 (2008) no. 3, pp. 288-306. http://geodesic.mathdoc.fr/item/AL_2008_47_3_a1/

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