Geodesic
Semimodular compact groups
Matematičeskie zametki, Tome 3 (1968) no. 5, pp. 503-509.

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A study of compact groups in which the lattice of all closed subgroups satisfies one of the following requirements: the Jordan–Dedekind condition for chains; semimodularity below; the same plus the existence of complements; the same plus the existence of relative complements is presented. 
@article{MZM_1968_3_5_a1,
     author = {Yu. N. Mukhin},
     title = {Semimodular compact groups},
     journal = {Matemati\v{c}eskie zametki},
     pages = {503--509},
     publisher = {mathdoc},
     volume = {3},
     number = {5},
     year = {1968},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1968_3_5_a1/}
}
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Yu. N. Mukhin. Semimodular compact groups. Matematičeskie zametki, Tome 3 (1968) no. 5, pp. 503-509. http://geodesic.mathdoc.fr/item/MZM_1968_3_5_a1/