Cartan invariants of group algebras of finite groups
Author:
Shigeo Koshitani
Journal:
Proc. Amer. Math. Soc. 124 (1996), 23192323
MSC (1991):
Primary 20C05, 20C20
MathSciNet review:
1328356
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Abstract: We give a result on Cartan invariants of the group algebra of a finite group over an algebraically closed field , which implies that if the Loewy length (socle length) of the projective indecomposable module corresponding to the trivial module is four, then has characteristic 2. The proof is independent of the classification of finite simple groups.
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 W. Feit, The representation theory of finite groups, NorthHolland, Amsterdam, 1982. MR 83g:20001
 [2]
 S. Koshitani, Group algebras of finite solvable groups with radicals of the fourth power zero, Proc. Royal Soc. Edinburgh 92A (1982), 205231. MR 84b:2007
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 P. Landrock, Finite group algebras and their modules, London Math. Soc. Lecture Note Series Vol.84, Cambridge, 1983. MR 85h:20002
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 P. Landrock, The Cartan matrix of a group algebra modulo any power of its radical, Proc. Amer. Math. Soc. 88 (1983), 205206. MR 84f:20010
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 G.O. Michler, Blocks and centers of group algebras, in Lectures on rings and modules, Springer Lecture Notes in Math. Vol.246, Springer, Berlin, 1972, pp.429563. MR 48:11274
 [6]
 W. Müller, Unzerlegbare Moduln über artinschen Ringen, Math. Z. 137 (1974), 197226. MR 50:4665
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 T. Okuyama, On blocks of finite groups with radical cube zero, Osaka J. Math. 23 (1986), 461465. MR 87k:20024
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 D.A.R. Wallace, Group algebras with radicals of square zero, Proc. Glasgow Math. Assoc. 5 (1962), 158159. MR 25:3986
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 P.J. Webb, The AuslanderReiten quiver of a finite group, Math. Z. 179 (1982), 97121. MR 83b:16029
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Additional Information
Shigeo Koshitani
Affiliation:
Department of Mathematics, Faculty of Science, Chiba University, Yayoicho, Chibacity, 263, Japan
Email:
koshitan@math.s.chibau.ac.jp
DOI:
http://dx.doi.org/10.1090/S0002993996034016
PII:
S 00029939(96)034016
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
