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Schur indices and irreducible character degrees in finite solvable groups

Published online by Cambridge University Press:  24 October 2008

R. Gow
R. Gow
Affiliation:
Mathematics Department, University College, Belfield, Dublin 4, Ireland
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Extract

Let G be a finite group and let Irr(G) denote the set of complex irreducible characters of G. Various authors have investigated the question of how information about the degrees of the characters in Irr (G) can provide information about the structure of G. Chapter 12 of [2] gives a survey of a number of results arising from such questions. Two well-known examples of theorems that relate character degrees and group structure are those due to Thompson (12·2 in [2]) and Itô (12.34 in [2]), which we recall here.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 105 , Issue 2 , March 1989 , pp. 237 - 240
Copyright
Copyright © Cambridge Philosophical Society 1989

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References

REFERENCES

[1]Gow, R.. Characters of solvable groups induced by linear characters of Hall subgroups. Arch. Math. (Basel) 40 (1983), 232–237.CrossRefGoogle Scholar
[2]Isaacs, M.. Character theory of finite groups (Academic Press, 1976).Google Scholar
[3]Isaacs, M.. Extensions of group representations over arbitrary fields. J. Algebra 68 (1981), 54–74.CrossRefGoogle Scholar
[4]Michler, G.. A finite simple group of Lie type has p-blocks of different defects, p ╪ 2. J. Algebra 104 (1986), 220–230.CrossRefGoogle Scholar