Geodesic
Infinite groups satisfying the normalizer condition for nonprimary subgroups
Matematičeskie zametki, Tome 19 (1976) no. 5, pp. 727-734

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In this paper we study infinite groups satisfying the normalizer condition for nonprimary subgroups. We show, in particular, that a nonprimary periodic group satisfying this condition is locally finite if the intersection of all its nonprimary subgroups is finite. We establish the local nilpotency of a nonperiodic group satisfying the normalizer condition for nonprimary subgroups. This implies the theorem of S. N. Chernikov which states that a nonperiodic group in which each infinite proper subgroup is different from its normalizer satisfies the normalizer condition. 
@article{MZM_1976_19_5_a7,
     author = {K. Sh. Kemkhadze},
     title = {Infinite groups satisfying the normalizer condition for nonprimary subgroups},
     journal = {Matemati\v{c}eskie zametki},
     pages = {727--734},
     publisher = {mathdoc},
     volume = {19},
     number = {5},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_19_5_a7/}
}
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K. Sh. Kemkhadze. Infinite groups satisfying the normalizer condition for nonprimary subgroups. Matematičeskie zametki, Tome 19 (1976) no. 5, pp. 727-734. http://geodesic.mathdoc.fr/item/MZM_1976_19_5_a7/