Geodesic
On the kernels of representations of finite groups
Glasgow mathematical journal, Tome 22 (1981) no. 2, pp. 151-154

Voir la notice de l'article provenant de la source Cambridge University Press

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). 
Koshitani, Shigeo. On the kernels of representations of finite groups. Glasgow mathematical journal, Tome 22 (1981) no. 2, pp. 151-154. doi: 10.1017/S0017089500004596
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[1] 1.Brauer, R., Some applications of the theory of blocks of characters of finite groups IV, J. Algebra 17 (1971), 489–521. Google Scholar

[2] 2.Brauer, R., On blocks and sections in finite groups I, Amer. J. Math. 89 (1967), 1115–1136. Google Scholar

[3] 3.Dornhoff, L., Group representation theory, parts A and B, (Dekker, 1971–1972). Google Scholar

[4] 4.Huppert, B., Endliche Gruppen I, (Springer-Verlag, 1967). Google Scholar | DOI

[5] 5.Isaacs, I. M. and Smith, S. D., A note on groups of p-length 1, J. Algebra 38 (1976), 531–535. Google Scholar | DOI

[6] 6.Michler, G. O., The kernel of a block of a group algebra, Proc. Amer. Math. Soc. 37 (1973), 47–49. Google Scholar

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