Geodesic
On primitive representations of soluble groups of finite rank
Sbornik. Mathematics, Tome 191 (2000) no. 11, pp. 1707-1748

Voir la notice de l'article provenant de la source Math-Net.Ru

In the paper it is proved, in particular, that a group is polycyclic if and only if it is soluble of finite rank, satisfies the ascending chain condition for normal subgroups and admits a faithful irreducible primitive representation over a field of characteristic zero. Methods are developed that enable one to study induced representations of nilpotent and soluble groups of finite rank. 
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     author = {A. V. Tushev},
     title = {On primitive representations of soluble groups of finite rank},
     journal = {Sbornik. Mathematics},
     pages = {1707--1748},
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     volume = {191},
     number = {11},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2000_191_11_a5/}
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A. V. Tushev. On primitive representations of soluble groups of finite rank. Sbornik. Mathematics, Tome 191 (2000) no. 11, pp. 1707-1748. http://geodesic.mathdoc.fr/item/SM_2000_191_11_a5/