More on the Schur subgroup
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- by Murray M. Schacher
- Proc. Amer. Math. Soc. 31 (1972), 15-17
- DOI: https://doi.org/10.1090/S0002-9939-1972-0291299-6
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Abstract:
Let $k$ be an abelian extension of the rational field $Q$. We show Schur’s subgroup $S(k)$ of the Bauer group $B(k)$ is usually of infinite index. Generators for $p$-torsion elements of $S(k)$ are found when $k$ is the cyclotomic field of $p$th roots of unity.References
- E. Artin and J. Tate, Class field theory, Harvard University, Cambridge, Mass., 1961.
- Mark Benard, The Schur subgroup. I, J. Algebra 22 (1972), 374–377. MR 302746, DOI 10.1016/0021-8693(72)90154-8
- Burton Fein and Murray Schacher, Embedding finite groups in rational division algebras. I, J. Algebra 17 (1971), 412–428. MR 272821, DOI 10.1016/0021-8693(71)90023-8
- K. L. Fields, On the Brauer-Speiser theorem, Bull. Amer. Math. Soc. 77 (1971), 223. MR 268293, DOI 10.1090/S0002-9904-1971-12691-5
- K. L. Fields, On the Schur subgroup, Bull. Amer. Math. Soc. 77 (1971), 477–478. MR 274608, DOI 10.1090/S0002-9904-1971-12746-5
- K. L. Fields and I. N. Herstein, On the Schur subgroup of the Brauer group, J. Algebra 20 (1972), 70–71. MR 289669, DOI 10.1016/0021-8693(72)90084-1
- Jean-Pierre Serre, Corps locaux, Publications de l’Institut de Mathématique de l’Université de Nancago, VIII, Hermann, Paris, 1962 (French). MR 0150130
- Ernst Witt, Die algebraische Struktur des Gruppenringes einer endlichen Gruppe über einem Zahlkörper, J. Reine Angew. Math. 190 (1952), 231–245 (German). MR 53944, DOI 10.1515/crll.1952.190.231
Bibliographic Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 31 (1972), 15-17
- DOI: https://doi.org/10.1090/S0002-9939-1972-0291299-6
- MathSciNet review: 0291299