Symmetric local algebras with $5$-dimensional center
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- by M. Chlebowitz and B. Külshammer PDF
- Trans. Amer. Math. Soc. 329 (1992), 715-731 Request permission
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 $8$.References
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Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 329 (1992), 715-731
- MSC: Primary 16P10; Secondary 16S34, 20C20
- DOI: https://doi.org/10.1090/S0002-9947-1992-1025752-1
- MathSciNet review: 1025752