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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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$\textbf {Q}(t)$ and $\textbf {Q}((t))$-admissibility of groups of odd order
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by Burton Fein and Murray Schacher PDF
Proc. Amer. Math. Soc. 123 (1995), 1639-1645 Request permission

Abstract:

Let $\mathbb {Q}(t)$ be the rational function field over the rationals, $\mathbb {Q}$, let $\mathbb {Q}((t))$ be the Laurent series field over $\mathbb {Q}$, and let $\mathcal {G}$ be a group of odd order. We investigate the following question: does there exist a finite-dimensional division algebra D central over $\mathbb {Q}(t)$ or $\mathbb {Q}((t))$ which is a crossed product for $\mathcal {G}$? If such a D exists, $\mathcal {G}$ is said to be $\mathbb {Q}(t)$-admissible (respectively, $\mathbb {Q}((t))$-admissible). We prove that if $\mathcal {G}$ is $\mathbb {Q}((t))$-admissible, then $\mathcal {G}$ is also $\mathbb {Q}(t)$-admissible; we also exhibit a $\mathbb {Q}(t)$-admissible group which is not $\mathbb {Q}((t))$-admissible.
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 1639-1645
  • MSC: Primary 12E15; Secondary 16K40
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1242083-3
  • MathSciNet review: 1242083