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