Geodesic
A description of solvable Lie groups with a given uniform subgroup
Sbornik. Mathematics, Tome 41 (1982) no. 1, pp. 83-99 
M. V. Milovanov. A description of solvable Lie groups with a given uniform subgroup. Sbornik. Mathematics, Tome 41 (1982) no. 1, pp. 83-99. http://geodesic.mathdoc.fr/item/SM_1982_41_1_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The article contains a method of describing all connected simply connected solvable Lie groups with a given uniform subgroup (not necessarily discrete). It is proved that such groups always form, up to isomorphism, no more than a countable set, and that this set decomposes into a finite number of classes of groups with isomorpbic commutator subgroups. Bibliography: 9 titles.

[1] L. Auslender, “An exposition of the structure of solvmanifolds”, Bull. Amer. Math. Soc., 79:2 (1973), 227–261 | DOI | MR

[2] M. V. Milovanov, “O razreshimykh gruppakh Li s zadannoi ravnomernoi podgruppoi”, DAN BSSR, 23:6 (1979), 485–487 | MR | Zbl

[3] M. V. Milovanov, “Opredelyaemost razreshimykh grupp Li ravnomernymi diskretnymi podgruppami”, DAN BSSR, 21:2 (1977), 108–111 | MR | Zbl

[4] M. V. Milovanov, “O schetnosti mnozhestva razreshimykh grupp Li s zadannoi reshetkoi”, DAN BSSR, 22:12 (1978), 1067–1068 | MR | Zbl

[5] V. V. Gorbatsevich, “O gruppakh Li, tranzitivnykh na kompaktnykh solvmnogoobraziyakh”, Izv. AN SSSR, seriya matem., 41 (1977), 285–308

[6] M. Ragunatan, Diskretnye podgruppy grupp Li, izd-vo “Mir”, Moskva, 1977 | MR

[7] G. D. Mostow, “Factor spaces of solvable groups”, Ann. Math., 60:1 (1954), 1–27 | DOI | MR | Zbl

[8] G. D. Mostow, “Representative functions on discrete groups and solvable arithmetic groups”, Amer. J. Math., 92:1 (1970), 1–32 | DOI | MR | Zbl

[9] H. Burbaki, Gruppy i algebry Li, izd-vo “Mir”, Moskva, 1976, glavy I–III | MR