Hostname: page-component-848d4c4894-ndmmz Total loading time: 0 Render date: 2024-06-01T05:14:42.741Z Has data issue: false hasContentIssue false
  • English
  • Français

On lower bounds for the radical of a block ideal in a finite p-solvable group

Published online by Cambridge University Press:  20 January 2009

Shigeo Koshitani
Shigeo Koshitani
Affiliation:
Department of Mathematics, Faculty of Science, Chiba University, Yayoi-Cho, Chiba-City, 260Japan
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.

Let F be any field of characteristic p > 0, G a finite p-solvable group, pa the order of Sylow p-subgroups of G, FG the group algebra of G over F, and J(FG) the Jacobson radical of FG. Following Wallace [11] we write t(G) for the least integer t≧1 such that J(FG)t = 0.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 27 , Issue 1 , February 1984 , pp. 65 - 71
Copyright
Copyright © Edinburgh Mathematical Society 1984

References

REFERENCES

1.Dornhoff, L., Group Representation Theory (part B, Marcel Dekker, New York, 1972).Google Scholar
2.Feit, W., The Representation Theory of Finite Groups (North-Holland, New York, 1982).Google Scholar
3.Fong, P., On the characters of p-solvable groups, Trans. Amer. Math. Soc. 98 (1961), 263–284.Google Scholar
4.Fong, P., Solvable groups and modular representation theory, Trans. Amer. Math. Soc. 103 (1962), 484–494.CrossRefGoogle Scholar
5.Gorenstein, D., Finite Groups (Harper & Row, New York, 1968)Google Scholar
6.Jennings, S. A., The structure of the group ring of a p-group over a modular field, Trans. Amer. Math. Soc. 50 (1941), 175–185.Google Scholar
7.Koshitani, S., Group algebras of finite p-solvable groups with radicals of the fourth power zero, Proc. Royal Soc. Edinburgh 92A (1982), 205–231.CrossRefGoogle Scholar
8.Michler, G. O., Blocks and centers of group algebras. Lectures on Rings and Modules (Lecture notes in math. 246, Springer, Berlin, 1972), 429–563.CrossRefGoogle Scholar
9.Rosenberg, A., Blocks and centres of group algebras, Math. Z. 76 (1961), 209–216.CrossRefGoogle Scholar
10.Tsushima, Y., On the second reduction theorem of P. Fong, Kumamoto J. Science (Math.) 13 (1978), 6–14.Google Scholar
11.Wallace, D. A. R., Lower bounds for the radical of the group algebra of a finite p-soluble group, Proc. Edinburgh Math. Soc. 16 (1968), 127–134.CrossRefGoogle Scholar
12.Watanabe, A., On Fong's reductions, Kumamoto J. Science (Math.) 13 (1979), 48–54.Google Scholar
13.Willems, W., On the projectives of a group algebra, Math. Z. 171 (1980), 163–174CrossRefGoogle Scholar