Abstract
Using the methods and results of preceding papers of the author (V. P. Platonov, The Tannaka-Artin problem and groups of projective conorms, Dokl. Akad. Nauk SSSR 222 (1975), 1229-1302="Soviet" Math. Dokl. 16 (1975), 782-786; The Tannaka-Artin problem and reduced -theory, Izv. Akad. Nauk SSSR Ser. Mat. 40 (1976), 227-261 = Math. USSR Izv. 10 (1976), 211-243), in the first part of this paper we find conditions under which the reduced Whitehead group is infinite, and in the second, larger part we give the solution of the Tannaka-Artin problem for cyclic algebras. In particular, we completely calculate the reduced Whitehead group for cyclic algebras over formal power series fields and construct cyclic algebras of arbitrary degree with Whitehead group that is arbitrarily large but finite, and also with infinite Whitehead group. Bibliography: 15 titles.
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