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
Let be a field of characteristic zero and suppose that is a -division algebra; i.e. a finite dimensional division algebra over with center . In Mollin  we proved that if contains no non-trivial odd order roots of unity, then every finite odd order subgroup of the multiplicative group of , 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.
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