Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-16T17:20:16.676Z Has data issue: false hasContentIssue false
  • English
  • Français

Irreducible representations of finitely generated nilpotent groups

Published online by Cambridge University Press:  24 October 2008

Daniel Segal
Daniel Segal
Affiliation:
Queen Mary College, London
Get access Rights & Permissions [Opens in a new window]

Extract

1. Introduction. It is well known that every finite-dimensional irreducible representation of a nilpotent group over an algebraically closed field is monomial, that is induced from a 1-dimensional representation of some subgroup. However, even a finitely generated nilpotent group in general has infinite-dimensional irreducible representations, and as a first step towards an understanding of these one wants to discover whether they too are necessarily monomial. The main point of this note is to show how far they can fail to be so.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 81 , Issue 2 , March 1977 , pp. 201 - 208
Copyright
Copyright © Cambridge Philosophical Society 1977

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Hall, P.On the finiteness of certain soluble groups. Proc. London Math. Soc. (3) 9 (1959), 595–622.CrossRefGoogle Scholar
(2)Passman, D. S.The algebraic structure of group rings. Academic Press (to appear).Google Scholar
(3)Roseblade, J. E.Group rings of polycyclic groups. J. Pure and Appl. Algebra 3 (1973), 307–328.CrossRefGoogle Scholar
(4)Zalesskii, A. E.Irreducible representations of finitely generated nilpotent torsion-free groups. (Russian.) Mat. Zametki 9 (1971), 199–210. Translation: Consultants Bureau, New York, 1971.Google Scholar