International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1984 / Article

Open Access

Volume 7 |Article ID 401870 | https://doi.org/10.1155/S0161171284000739

R. A. Mollin, "Admissible groups, symmetric factor sets, and simple algebras", International Journal of Mathematics and Mathematical Sciences, vol. 7, Article ID 401870, 5 pages, 1984. https://doi.org/10.1155/S0161171284000739

Admissible groups, symmetric factor sets, and simple algebras

Received22 Jun 1983

Abstract

Let K be a field of characteristic zero and suppose that D is a K-division algebra; i.e. a finite dimensional division algebra over K with center K. In Mollin [1] we proved that if K contains no non-trivial odd order roots of unity, then every finite odd order subgroup of D* the multiplicative group of D, is cyclic. The first main result of this paper is to generalize (and simplify the proof of) the above. Next we generalize and investigate the concept of admissible groups. Finally we provide necessary and sufficient conditions for a simple algebra, with an abelian maximal subfield, to be isomorphic to a tensor product of cyclic algebras. The latter is achieved via symmetric factor sets.

Copyright © 1984 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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