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On the field of a $ 2$-block


Author: B. G. Basmaji
Journal: Proc. Amer. Math. Soc. 83 (1981), 471-475
MSC: Primary 20C15; Secondary 20C20
DOI: https://doi.org/10.1090/S0002-9939-1981-0627672-9
MathSciNet review: 627672
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Abstract: For a $ p$-block $ B$ satisfying some conditions, a field $ Q(B)$ is defined. It is proved that for a $ 2$-block $ B$ of a finite metabelian group $ G$, $ Q(B) = Q(\theta )$ for some irreducible character $ \theta $ in $ B$ if the $ 2$-Sylow subgroup $ P$ of the commutator group $ G'$ is cyclic. This is shown to be false in general.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0627672-9
Keywords: Characters, real characters, $ p$-blocks, real $ p$-blocks, $ 2$-rational characters, modular and ordinary representations
Article copyright: © Copyright 1981 American Mathematical Society

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