Geodesic
Topological groups with the compactness condition for conjugate classes
Matematičeskie zametki, Tome 21 (1977) no. 2, pp. 251-257.

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The compactness of a locally compact $RI$-group satisfying the compactness condition for conjugate classes is proved. 
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     author = {V. M. Poletskikh},
     title = {Topological groups with the compactness condition for conjugate classes},
     journal = {Matemati\v{c}eskie zametki},
     pages = {251--257},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1977_21_2_a13/}
}
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V. M. Poletskikh. Topological groups with the compactness condition for conjugate classes. Matematičeskie zametki, Tome 21 (1977) no. 2, pp. 251-257. http://geodesic.mathdoc.fr/item/MZM_1977_21_2_a13/