Hostname: page-component-745bb68f8f-g4j75 Total loading time: 0 Render date: 2025-02-02T22:19:03.315Z Has data issue: false hasContentIssue false
  • English
  • Français

On the determination of the ramification index in Clifford's theorem

Published online by Cambridge University Press:  13 July 2011

Robert W. van der Waall
Robert W. van der Waall
Affiliation:
Mathematisch InstituutUniversiteit van AmsterdamRoetersstraat 151018 WB Amsterdam, The Netherlands
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let K be a field, G a finite group, V a (right) KG-module. If H is a subgroup of G, then, restricting the action of G on V to H, V is also a KH-module. Notation: VH.

Suppose N is a normal subgroup of G. The KN-module VN is not irreducible in general, even when V is irreducible as KG-module. A part of the well-known theorem of A. H. Clifford [1, V.17.3] yields the following.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 31 , Issue 3 , October 1988 , pp. 469 - 474
Copyright
Copyright © Edinburgh Mathematical Society 1988

References

REFERENCES

1.Huppert, B., Endliche Gruppen I (Springer-Verlag, Berlin-Heidelberg-New York, 1967).Google Scholar
2.Huppert, B. and Blackburn, N., Finite Groups II (Springer-Verlag, Berlin-Heidelberg-New York, 1982).Google Scholar
3.Isaacs, I. M., Character Theory of Finite Groups (Academic Press, New York-London, 1976).Google Scholar
4.Vander, R. W.Waall, Minimal non-M-groups, Indag. Math. 42 (1980), 93–106.CrossRefGoogle Scholar
5.Van Der Waall, R. W., On Clifford's theorem and ramification indices for symplectic modules over a finite field, Proc. Edinburgh Math. Soc. 30 (1987), 153–167.Google Scholar
6.Willems, W., Induzierte und eingeschränkte Moduln über Gruppenringen (Diplomarbeit, Mainz, 1973).Google Scholar