Symmetric local algebras with 5-dimensional center

Chlebowitz, M.; Külshammer, B.

doi:10.1090/S0002-9947-1992-1025752-1

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 $8$.

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