Geodesic
Groups with given properties of finite subgroups
Algebra i logika, Tome 51 (2012) no. 3, pp. 321-330

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Suppose that in every finite even order subgroup $F$ of a periodic group $G$, the equality $[u,x]^2=1$ holds for any involution $u$ of $F$ and for an arbitrary element $x$ of $F$. Then the subgroup $I$ generated by all involutions in $G$ is locally finite and is a $2$-group. In addition, the normal closure of every subgroup of order $2$ in $G$ is commutative.
Keywords: periodic group, finite group, locally finite group, involution. 
@article{AL_2012_51_3_a1,
     author = {D. V. Lytkina and V. D. Mazurov},
     title = {Groups with given properties of finite subgroups},
     journal = {Algebra i logika},
     pages = {321--330},
     publisher = {mathdoc},
     volume = {51},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2012_51_3_a1/}
}
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D. V. Lytkina; V. D. Mazurov. Groups with given properties of finite subgroups. Algebra i logika, Tome 51 (2012) no. 3, pp. 321-330. http://geodesic.mathdoc.fr/item/AL_2012_51_3_a1/