and -admissibility of groups of odd order

Authors:
Burton Fein and Murray Schacher

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

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be the rational function field over the rationals, , let be the Laurent series field over , and let be a group of odd order. We investigate the following question: does there exist a finite-dimensional division algebra *D* central over or which is a crossed product for ? If such a *D* exists, is said to be -admissible (respectively, -admissible). We prove that if is -admissible, then is also -admissible; we also exhibit a -admissible group which is not -admissible.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1995-1242083-3

Keywords:
Division algebra,
Brauer group,
admissible,
crossed product

Article copyright:
© Copyright 1995
American Mathematical Society