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On the divisible part of the Brauer group of a field


Author: Tilmann Würfel
Journal: Proc. Amer. Math. Soc. 84 (1982), 173-174
MSC: Primary 12G05; Secondary 20E18
DOI: https://doi.org/10.1090/S0002-9939-1982-0637162-6
MathSciNet review: 637162
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Abstract: For a field $ k$ and an odd prime $ p \ne \operatorname{char} (k)$ such that the $ p$-primary component $ B{(k)_{(p)}}$ of the Brauer group $ B(k)$ of $ k$ is not zero there exists a finite extension $ k/k$ such that $ B{(k)_{(p)}}$ contains a nontrivial divisible subgroup.


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DOI: https://doi.org/10.1090/S0002-9939-1982-0637162-6
Keywords: Brauer group of a field, profinite group, divisible group
Article copyright: © Copyright 1982 American Mathematical Society