Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

More on the Schur subgroup


Author: Murray M. Schacher
Journal: Proc. Amer. Math. Soc. 31 (1972), 15-17
DOI: https://doi.org/10.1090/S0002-9939-1972-0291299-6
MathSciNet review: 0291299
Full-text PDF Free Access

Abstract | References | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] E. Artin and J. Tate, Class field theory, Harvard University, Cambridge, Mass., 1961.
  • [2] M. Benard, The Schur subgroup. I, J. Algebra (to appear). MR 0302746 (46:1889)
  • [3] B. Fein and M. Schacher, Embedding finite groups in rational division algebras. I, J. Algebra 17 (1971), 412-428. MR 0272821 (42:7702)
  • [4] K. L. Fields, On the Brauer-Speiser theorem, Bull. Amer. Math. Soc. 77 (1971), 223. MR 0268293 (42:3192)
  • [5] -, On the Schur subgroup, Bull. Amer. Math. Soc. 77 (1971), 477-478. MR 0274608 (43:371)
  • [6] K. L. Fields and I. N. Herstein, On the Schur subgroup of the Brauer group, J. Algebra (to appear). MR 0289669 (44:6857)
  • [7] J.-P. Serre, Corps locaux, Publ. Inst. Math. Univ. Nancago, VIII, Actualités Sci. Indust., no. 1296, Hermann, Paris, 1962. MR 27 #133. MR 0150130 (27:133)
  • [8] E. Witt, Die Algebraische Struktur des Gruppenringes einer endlichen Gruppe über einem Zahlkörper, J. Reine Angew. Math. 190 (1952), 231-245. MR 14, 845. MR 0053944 (14:845a)


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0291299-6
Keywords: Brauer group, cyclotomic, exponent, group algebra, Hasse invariant, index, prime, Schur subgroup, tamely ramified, unramified
Article copyright: © Copyright 1972 American Mathematical Society

American Mathematical Society