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The structure of the multiplicative group of residue classes modulo

Published online by Cambridge University Press:  22 January 2016

Norikata Nakagoshi
Norikata Nakagoshi*
Affiliation:
Department of Mathematics, College of Liberal Arts, Toyama University
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Let k be an algebraic number field of finite degree and be a prime ideal of k, lying above a rational prime p. We denote by G () the multiplicative group of residue classes modulo (N ≧ 0) which are relatively prime to . The structure of G () is well-known, when N = 0, or k is the rational number field Q. If k is a quadratic number field, then the direct decomposition of G () is determined by A. Ranum [6] and F.H-Koch [4] who gives a basis of a group of principal units in the local quadratic number field according to H. Hasse [2]. In [5, Theorem 6.2], W. Narkiewicz obtains necessary and sufficient conditions so that G () is cyclic, in connection with a group of units in the -adic completion of k.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 73 , March 1979 , pp. 41 - 60
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1979

References

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