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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Cartan invariants
of group algebras of finite groups


Author: Shigeo Koshitani
Journal: Proc. Amer. Math. Soc. 124 (1996), 2319-2323
MSC (1991): Primary 20C05, 20C20
MathSciNet review: 1328356
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Abstract: We give a result on Cartan invariants of the group algebra $kG$ of a finite group $G$ over an algebraically closed field $k$, which implies that if the Loewy length (socle length) of the projective indecomposable $kG$-module corresponding to the trivial $kG$-module is four, then $k$ has characteristic 2. The proof is independent of the classification of finite simple groups.


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Additional Information

Shigeo Koshitani
Affiliation: Department of Mathematics, Faculty of Science, Chiba University, Yayoi-cho, Chiba-city, 263, Japan
Email: koshitan@math.s.chiba-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03401-6
PII: S 0002-9939(96)03401-6
Received by editor(s): August 17, 1994
Received by editor(s) in revised form: February 7, 1995
Additional Notes: Supported in part by the Alexander von Humboldt Foundation, the Mathematical Prizes Fund, the University of Oxford and the Sasakawa Foundation.
Dedicated: Dedicated to Professor Takeshi Kondo on his 60th birthday
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1996 American Mathematical Society