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A remark on the nilpotency index of the radical of a group algebra of a p-solvable group

Published online by Cambridge University Press:  20 January 2009

Shigeo Koshitani
Shigeo Koshitani
Affiliation:
Department of MathematicsFaculty of ScienceChiba University1–33, Yayoi-ChoChiba-City, 260, Japan
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Let K be a field of characteristic p>0, G a finite p-solvable group, P a p-Sylow subgroup of G of order pa, KG the group algebra of G over K, and J(KG) the Jacobson radical of KG. In the present paper we study the nilpotency index t(G) of J(KG), which is the least positive integer t with J(KG)t= 0. Since J(EG) = E⊗KJ(KG) for any extension field E of K (cf. [7, Proposition 12.11]), we may assume that K is algebraically closed.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 25 , Issue 1 , February 1982 , pp. 31 - 34
Copyright
Copyright © Edinburgh Mathematical Society 1982

References

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