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

Character table and blocks of finite simple triality groups $ \sp 3D\sb 4(q)$


Authors: D. I. Deriziotis and G. O. Michler
Journal: Trans. Amer. Math. Soc. 303 (1987), 39-70
MSC: Primary 20C15; Secondary 20C20, 20G40
MathSciNet review: 896007
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Abstract: Based on recent work of Spaltenstein [14] and the Deligne-Lusztig theory of irreducible characters of finite groups of Lie type, in this paper the character table of the finite simple groups $ {}^3{D_4}(q)$ is given. As an application we obtain a classification of the irreducible characters of $ {}^3{D_4}(q)$ into $ r$-blocks for all primes $ r > 0$. This enables us to verify Brauer's height zero conjecture, his conjecture on the bound of irreducible characters belonging to a give block, and the Alperin-McKay conjecture for the simple triality groups $ {}^3{D_4}(q)$. It also follows that for every prime $ r$ there are blocks of defect zero in $ {}^3{D_4}(q)$.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1987-0896007-9
PII: S 0002-9947(1987)0896007-9
Article copyright: © Copyright 1987 American Mathematical Society