The linear and quadratic Schur subgroups over the integers of a number field
Author:
Carl R. Riehm
Journal:
Proc. Amer. Math. Soc. 107 (1989), 8387
MSC:
Primary 11R65; Secondary 11R54, 13A20, 20C10
MathSciNet review:
979218
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Abstract: Let be an algebraic number field and let be a ring of integers in (where is a set of primes of containing all the archimedean primes); that is to say, is a Dedekind domain whose field of quotients is . In analogy with a theorem of T. Yamada in the case of a field of characteristic 0, it is shown that if is the Schur subgroup of the Brauer group and if , where is any field containing the maximal abelian extension of in , then , i.e. the Brauer classes in are those obtained from by extension of the scalars to . A similar theorem is proved as well in the case of the Schur subgroup of the quadratic Brauer group , where is an involution of .
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 I. M. Isaacs, Character theroy of finite groups, Academic Press, New York, 1976. MR 0460423 (57:417)
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 T. Yamada, The Schur subgroup of the Brauer group, Lecture Notes in Math., vol. 397, SpringerVerlag, New York, 1974. MR 0347957 (50:456)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939198909792180
PII:
S 00029939(1989)09792180
Keywords:
Schur subgroup,
integral Brauer group,
integral representations,
representations of finite groups,
quadratic Brauer group,
Azumaya algebras,
algebraic number fields
Article copyright:
© Copyright 1989
American Mathematical Society
