Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-15T08:50:58.875Z Has data issue: false hasContentIssue false

On the kernels of representations of finite groups II

Published online by Cambridge University Press:  18 May 2009

Shigeo Koshitani
Affiliation:
Department of MathematicsFaculty of ScienceChiba University1-33 Yayoi-ChoChiba-City 260, Japan
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.

About fifteen years ago I. M. Isaacs and S. D. Smith [9] gave several character-theoretic characterizations of finite p-solvable groups G with p-length one, where p is a prime number. They proved that for a finite group G with a Sylow p-subgroup P, the following four conditions (a)–(d) are equivalent.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 1990

References

REFERENCES

1.Alperin, J. L., Weights for finite groups, in The Arcata Conference on Representations of Finite Groups, Proc. Sympos. Pure Math. 47 (Part 1) (1987), 369379.CrossRefGoogle Scholar
2.Brauer, R., Some applications of the theory of blocks of characters of finite groups IV, J. Algebra 17 (1971), 489521.CrossRefGoogle Scholar
3.Broué, M. and Puig, L., A Frobenius theorem for blocks, Invent. Math. 56 (1980), 117128.CrossRefGoogle Scholar
4.Curtis, C. W. and Reiner, I., Methods of representation theory vol. II (Wiley-Interscience, 1987).Google Scholar
5.Dornhoff, L., Group representation theory (Dekker, 1972).Google Scholar
6.Feit, W., The representation theory of finite groups (North-Holland, 1982).Google Scholar
7.Hamernik, W. and Michler, G. O., On vertices of simple modules in p-solvable groups, Mitt. Math. Sem. Giessen 121 (1976), 147162.Google Scholar
8.Isaacs, I. M., Character theory of finite groups (Academic Press, 1976).Google Scholar
9.Isaacs, I. M. and Smith, S. D., A note on groups of p-length 1, J. Algebra 38 (1976), 531535.CrossRefGoogle Scholar
10.Knörr, R., Blocks, , vertices and normal subgroups, Math. Z. 148 (1976), 5360.CrossRefGoogle Scholar
11.Koshitani, S., On the kernels of representations of finite groups, Glasgow Math. J. 22 (1981), 151154.CrossRefGoogle Scholar
12.Michler, G. O., The kernel of a block of a group algebra, Proc. Amer. Math. Soc. 37 (1973), 4749.CrossRefGoogle Scholar
13.Morita, K., On group rings over a modular field which possess radicals expressible as principal ideals, Sci. Rep. Tokyo Bunrika Daigaku. Sect. A 4 (1951), 177194.Google Scholar
14.Motose, K. and Ninomiya, Y., On the subgroups H of a group G such that J(KH)KGJ(KG), Math. J. Okayama Univ. 17 (1975), 171176.Google Scholar
15.Okuyama, T., p-radical groups are p-solvable, Osaka J. Math. 23 (1986), 467469.Google Scholar
16.Pahlings, H., Groups with faithful blocks, Proc. Amer. Math. Soc. 51 (1975), 3740.CrossRefGoogle Scholar
17.Pahlings, H., Normal p-complements and irreducible characters, Math. Z. 154 (1977), 243246.CrossRefGoogle Scholar
18.Willems, W., On the projectives of a group algebra, Math. Z. 171 (1980), 163174.CrossRefGoogle Scholar