Cartan invariants of group algebras of finite groups
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- by Shigeo Koshitani PDF
- Proc. Amer. Math. Soc. 124 (1996), 2319-2323 Request permission
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.References
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Additional Information
- Shigeo Koshitani
- Affiliation: Department of Mathematics, Faculty of Science, Chiba University, Yayoi-cho, Chiba-city, 263, Japan
- MR Author ID: 202274
- Email: koshitan@math.s.chiba-u.ac.jp
- 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.
- Communicated by: Ronald M. Solomon
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 2319-2323
- MSC (1991): Primary 20C05, 20C20
- DOI: https://doi.org/10.1090/S0002-9939-96-03401-6
- MathSciNet review: 1328356
Dedicated: Dedicated to Professor Takeshi Kondo on his 60th birthday