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On the kernels of representations of finite groups

Published online by Cambridge University Press:  18 May 2009

Shigeo Koshitani
Shigeo Koshitani
Affiliation:
Department of Mathematics, Chiba University, 1–33, Yauoi-cho Chiba-city, 280, Japan
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Let G be a finite group and p a prime number. About five years ago I. M. Isaacs and S. D. Smith [5] gave several character-theoretic characterizations of finite p-solvable groups with p-length 1. Indeed, they proved that if P is a Sylow p-subgroup of G then the next four conditions (l)–(4) are equivalent:

(1) G is p-solvable of p-length 1.

(2) Every irreducible complex representation in the principal p-block of G restricts irreducibly to NG(P).

(3) Every irreducible complex representation of degree prime to p in the principal p-block of G restricts irreducibly to NG(P).

(4) Every irreducible modular representation in the principal p-block of G restricts irreducibly to NG(P).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 22 , Issue 2 , July 1981 , pp. 151 - 154
Copyright
Copyright © Glasgow Mathematical Journal Trust 1981

References

REFERENCES

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