## $\textbf {Q}(t)$ 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