Geodesic
Representations of infinite soluble groups
Glasgow mathematical journal, Tome 24 (1983) no. 1, pp. 43-52

Voir la notice de l'article provenant de la source Cambridge University Press

The purpose of this paper is to study the following two questions.(1) When does the group algebra of a soluble group have infinite dimensional irreducible modules?(2) When is the group algebra of a torsion free soluble group primitive?In relation to the first question, Roseblade [13] has proved that if G is a polycyclic group and k an absolute field then all irreducible kG-modules are finite dimensional. Here we prove a converse. 
Musson, Ian M. Representations of infinite soluble groups. Glasgow mathematical journal, Tome 24 (1983) no. 1, pp. 43-52. doi: 10.1017/S0017089500005048
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[1] 1.Bergman, G. M., The logarithmic limit set of an algebraic variety, Trans. Amer. Math. Soc. 157 (1971), 459–469. Google Scholar

[2] 2.Brown, K. A., Primitive group rings of soluble groups, Arch. Math. (Basel) 36 (1981), 404–413. Google Scholar

[3] 3.Farkas, D. R., Group rings, an annotated questionaire, Comm. Alg. 8 (1980), 585–602. Google Scholar

[4] 4.Farkas, D. R. and Passman, D. S., Primitive Noetherian group rings, Comm. Alg. 5 (1978), 301–315. Google Scholar

[5] 5.Farkas, D. R. and Snider, R. L., Group algebras whose simple modules are injective, Trans. Amer. Math. Soc. 194 (1974), 241–248. Google Scholar

[6] 6.Fuchs, L., Abelian groups (Pergamon, 1960). Google Scholar

[7] 7.Hartley, B., Injective modules over group rings, Quart. J. Math. 28 (1977), 1–29. Google Scholar

[8] 8.Irving, R. S., Some more primitive group rings, Israel J. Math. 37 (1980), 331–350. Google Scholar | DOI

[9] 9.Jategaonkar, A. V., Integral group rings of polycyclic-by-finite groups, J. Pure and Applied Algebra 4 (1974), 337–343. Google Scholar | DOI

[10] 10.Kaplansky, I., Commutative rings (University of Chicago Press, 1974). Google Scholar

[11] 11.Passman, D. S., The algebraic structure of group rings(Wiley-Interscience, 1977). Google Scholar

[12] 12.Robinson, D. J. S., Finiteness conditions and generalized soluble groups, parts 1 and 2 (Springer-Verlag, 1972). Google Scholar

[13] 13.Roseblade, J. E., Group rings of polycyclic groups, J. Pure and Applied Algebra 3 (1974), 307–328. Google Scholar

[14] 14.Roseblade, J. E., Prime ideals in group rings of polycyclic groups, Proc. London Math. Soc. 36 (1978), 385–447. Google Scholar | DOI

[15] 15.Snider, R. L., Soluble groups whose representations are finite dimensional, Abstracts Amer. Math. Soc.(1980), Abstract 775–A6, page 250. Google Scholar

[16] 16.Wehrfritz, B. A. F., Infinite linear groups (Springer-Verlag, 1973). Google Scholar

[17] 17.Wehrfritz, B. A. F., Groups whose irreducible representations have finite degree I, Math. Proc. Cambridge Philos. Soc. 90 (1981), 411–421. Google Scholar | DOI

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