Geodesic
Locally compact groups with complementary closed subgroups
Matematičeskie zametki, Tome 6 (1969) no. 6, pp. 641-649.

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Topological groups with complementary closed abelian subgroups and with complementary monothetic subgroups are considered. 
@article{MZM_1969_6_6_a0,
     author = {T. M. Lozben'},
     title = {Locally compact groups with complementary closed subgroups},
     journal = {Matemati\v{c}eskie zametki},
     pages = {641--649},
     publisher = {mathdoc},
     volume = {6},
     number = {6},
     year = {1969},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1969_6_6_a0/}
}
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T. M. Lozben'. Locally compact groups with complementary closed subgroups. Matematičeskie zametki, Tome 6 (1969) no. 6, pp. 641-649. http://geodesic.mathdoc.fr/item/MZM_1969_6_6_a0/