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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Symmetric local algebras with $ 5$-dimensional center


Authors: M. Chlebowitz and B. Külshammer
Journal: Trans. Amer. Math. Soc. 329 (1992), 715-731
MSC: Primary 16P10; Secondary 16S34, 20C20
MathSciNet review: 1025752
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Abstract: We prove that a symmetric split local algebra whose center is $ 5$-dimensional has dimension $ 5$ or $ 8$. This implies that the defect groups of a block of a finite group containing exactly five irreducible Frobenius characters and exactly one irreducible Brauer character have order $ 5$ or are nonabelian of order $ 8$.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1992-1025752-1
PII: S 0002-9947(1992)1025752-1
Article copyright: © Copyright 1992 American Mathematical Society