The p-Rank of Tame Kernels of Pure Quintic Fields

Abstract

Let F be a pure quintic field. In this paper, we present some results for the p-rank of K2𝒪F, where p is an odd prime number. In particular, the 5-rank of K2𝒪F is studied by the reflection theorem. Some explicit results on the 5-rank of K2𝒪F are given in some special cases.