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Proceedings of ASARC Workshop Daecheon & Muju 2009
(2009 / vol.11 / no.2)
On the Ideal Class Groups for Cyclotomic Fields
Sey Yoon Kim
Pages. 9-13   



Let $p$ be an odd prime number, and put $K:={mathbb Q}(e^{2pi i/p})$. We shall review the basic structure of the Sylow $p$-subgroup of the ideal class group for the number field ${mathbb Q}(e^{2pi i/p})$ regarded as a ${mathbb F}_p[mathrm{Gal}(K/{mathbb Q})]$-module, and recall Vandiver's conjecture. Then we shall consider a problem which naturally arises from studying the conjecture.



1. Introduction
2. The Bernoulli Numbers
3. The Basic Structure of ${mathcal A}$
4. Vandiver's Conjecture and $K$-groups of ${mathbb Z}$
5. Problems Related to Vandiver's Conjecture