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manuscripta mathematica

, Volume 24, Issue 2, pp 173–177 | Cite as

The elements of K2(ℤs)

  • Jürgen Hurrelbrink
Article

Abstract

Let S={p1,...,ps} be a set of rational primes,\(\mathbb{Z}_S : = \mathbb{Z}[\frac{1}{{P_1 }},...,\frac{1}{{P_5 }}]\). One has K2(ℤs)≅K2(ℤsu{2} and we want to assume 2 ∈ S. It is snown that every element of K2(ℤS) is a Dehnis-Stein-symbol <a,b>, 1+ab being a unit of ℤS.

Here b ∈ ℤ can be determined concretely, depending only on S, and we obtain a normal form of the elements of K2(Q) as Steinberg-symbols, which is unique in some way and expresses the quadratic reciprocity law.

Keywords

Normal Form Number Theory Algebraic Geometry Topological Group Quadratic Reciprocity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    DENNIS, R.K., STEIN, M.R.: The functor K2: a survey of computations and problems. Algebraic K-Theory II. Springer Lect. Notes in Math.342, 243–280 (1973)Google Scholar
  2. [2]
    LENSTRA, H. W. Jr.: K2 of a global field consists of symbols. Algebraic K-Theory. Springer Lect. Notes in Math.551, 69–73, (1976)Google Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • Jürgen Hurrelbrink
    • 1
  1. 1.Fakultät für MathematikBielefeld 1

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