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Rational projective representations of finite groups

Published online by Cambridge University Press:  24 October 2008

J. F. Humphreys
J. F. Humphreys
Affiliation:
University of Liverpool
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Extract

Let G bea finite group, let C1, …, Cn be the cyclic subgroups of G and let 1i be the identity linear character of Ci (1 ≤ i ≤ n). It is a well-known result of Artin ((l), 39·1) that a character x of a linear representation of G over the rational numbers may be written

where a1, …, an are integers. In this note, we establish an analogue of this result for characters of projective representations over the rational numbers.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 86 , Issue 3 , November 1979 , pp. 413 - 419
Copyright
Copyright © Cambridge Philosophical Society 1979

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References

REFERENCES

(1)Curtis, C. W. and Reiner, I.Representation theory of finite groups and associative algebras (New York, Interscienoe, 1962).Google Scholar
(2)Haggarty, R. J. and Humphreys, J. F.Projective characters of finite groups. Proc. London Math. Soc. (3) 36 (1978), 176–192.CrossRefGoogle Scholar