The 2-Sylow subgroups of the tame kernel of imaginary quadratic fields

Hourong Qin

ArticleOriginal scientific text

Title

The 2-Sylow subgroups of the tame kernel of imaginary quadratic fields

Authors ¹

Affiliations

Department of Mathematics, Nanjing University, Nanjing, 210008, P.R. China

Abstract

1. Introduction. Let F be a number field and

O_{F}

the ring of its integers. Many results are known about the group

K ₂ O_{F}

, the tame kernel of F. In particular, many authors have investigated the 2-Sylow subgroup of

K ₂ O_{F}

. As compared with real quadratic fields, the 2-Sylow subgroups of

K ₂ O_{F}

for imaginary quadratic fields F are more difficult to deal with. The objective of this paper is to prove a few theorems on the structure of the 2-Sylow subgroups of

K ₂ O_{F}

for imaginary quadratic fields F. In our Ph.D. thesis (see [11]), we develop a method to determine the structure of the 2-Sylow subgroups of

K ₂ O_{F}

for real quadratic fields F. The present paper is motivated by some ideas in the above thesis.

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Title

The 2-Sylow subgroups of the tame kernel of imaginary quadratic fields

Affiliations

Abstract

Bibliography