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The nilpotency index of the radicals of group algebras of finite groups whose Sylow 3-subgroups are extra-special of order 27 of exponent 3

Published online by Cambridge University Press:  14 November 2011

Shigeo Koshitani
Shigeo Koshitani
Affiliation:
Department of Mathematics, Faculty of Science, Chiba University, Yayoi-cho, Chiba-city, 260, Japan
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Synopsis

Let J(FG) be the Jacobson radical of the group algebra FG of a finite groupG with a Sylow 3-subgroup which is extra-special of order 27 of exponent 3 over a field F of characteristic 3, and let t(G) be the least positive integer t with J(FG)t = 0. In this paper, we prove that t(G) = 9 if G has a normal subgroup H such that (|G:H|, 3) = 1 and if H is either 3-solvable, SL(3,3) or the Tits simple group 2F4(2)'.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 108 , Issue 1-2 , 1988 , pp. 117 - 132
Copyright
Copyright © Royal Society of Edinburgh 1988

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