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Nilpotency indices of the radicals of finite p-solvable group algebras, I

Part of: Rings and algebras arising under various constructions Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

Yasushi Ninomiya
Yasushi Ninomiya
Affiliation:
Department of Mathematical Sciences Faculty of Science Shinshu University Matsumoto390-8621Japan e-mail: [email protected]
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Abstract

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Let k be a field of characteristic p > 0, G a finite p-solvable group and pm the highest power of p dividing the order of G. We denote by t(G) the nilpotency index of the (Jacobson) radical of the group algebra k[G]. The groups G with t(G) ≥ pm−1 are already classified. The aim of this paper is to classify the p-solvable groups G with pm−2 < t(G) < pm−1 for p odd.

MSC classification

Secondary: 20C05: Group rings of finite groups and their modules 16S34: Group rings , Laurent polynomial rings
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 71 , Issue 1 , August 2001 , pp. 117 - 133
Copyright
Copyright © Australian Mathematical Society 2001

References

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