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Representations of infinite soluble groups

Published online by Cambridge University Press:  18 May 2009

Ian M. Musson
Ian M. Musson
Affiliation:
University of Wisconsin-Madison Madison, WI 53706USA
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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.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 24 , Issue 1 , January 1983 , pp. 43 - 52
Copyright
Copyright © Glasgow Mathematical Journal Trust 1983

References

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