Geodesic
2-groups with given properties of finite subgroups
Vladikavkazskij matematičeskij žurnal, Tome 13 (2011) no. 4, pp. 35-39

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A local finiteness is proved of 2-groups, all of whose finite subgroups (a) are nilpotent of class 2 or (b) belong to a variety defined by the law $[x,y]^2=1$. Besides, it is proved that the order of the derived subgroup of a 2-group $G$ is at most 2 if the order of every conjugacy class of every finite subgroup of $G$ is at most 2. 
@article{VMJ_2011_13_4_a3,
     author = {D. V. Lytkina},
     title = {2-groups with given properties of finite subgroups},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {35--39},
     publisher = {mathdoc},
     volume = {13},
     number = {4},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2011_13_4_a3/}
}
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D. V. Lytkina. 2-groups with given properties of finite subgroups. Vladikavkazskij matematičeskij žurnal, Tome 13 (2011) no. 4, pp. 35-39. http://geodesic.mathdoc.fr/item/VMJ_2011_13_4_a3/