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Representations of infinite soluble groups
Published online by Cambridge University Press: 18 May 2009
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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.
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- Copyright © Glasgow Mathematical Journal Trust 1983
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