Admissible groups, symmetric factor sets, and simple algebras
Date
1984-01-01
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
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.
Description
Keywords
Citation
R. A. Mollin, “Admissible groups, symmetric factor sets, and simple algebras,” International Journal of Mathematics and Mathematical Sciences, vol. 7, no. 4, pp. 707-711, 1984. doi:10.1155/S0161171284000739