Geodesic
Periodic groups saturated with $L_3(2^m)$
Algebra i logika, Tome 46 (2007) no. 5, pp. 606-626

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Let $\mathfrak M$ be a set of finite groups. A group $G$ is saturated with groups from $\mathfrak M$ if every finite subgroup of $G$ is contained in a subgroup isomorphic to some member of $\mathfrak M$. It is proved that a periodic group $G$ saturated with groups from the set $\{L_3(2^m)\mid m=1,2,\dots\}$ is isomorphic to $L_3(Q)$, for a locally finite field $Q$ of characteristic 2; in particular, it is locally finite.
Keywords: periodic group, locally finite group. 
@article{AL_2007_46_5_a4,
     author = {D. V. Lytkina and V. D. Mazurov},
     title = {Periodic groups saturated with~$L_3(2^m)$},
     journal = {Algebra i logika},
     pages = {606--626},
     publisher = {mathdoc},
     volume = {46},
     number = {5},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2007_46_5_a4/}
}
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D. V. Lytkina; V. D. Mazurov. Periodic groups saturated with $L_3(2^m)$. Algebra i logika, Tome 46 (2007) no. 5, pp. 606-626. http://geodesic.mathdoc.fr/item/AL_2007_46_5_a4/