• Corpus ID: 115165499

# K_1 of some noncommutative group rings

@article{Kakde2010K\_1OS,
title={K\_1 of some noncommutative group rings},
author={Mahesh Kakde},
journal={arXiv: Number Theory},
year={2010}
}
• M. Kakde
• Published 19 March 2010
• Mathematics
• arXiv: Number Theory
In this article I generalise previous computations (by K. Kato, T. Hara and myself) of K_1 (only up to p-power torsion) of p-adic group rings of finite non-abelian p-groups in terms of p-adic group rings of abelian subquotients of the group. Such computation have applications in non-commutative Iwasawa theory due to a strategy proposed by D. Burns, K. Kato (and a modification by T. Hara) for deducing non-commutative main conjectures from commutative main conjectures and certain congruences…
3 Citations
The main conjecture of Iwasawa theory for totally real fields
Let p be an odd prime. Let $\mathcal{G}$ be a compact p-adic Lie group with a quotient isomorphic to ℤp. We give an explicit description of K1 of the Iwasawa algebra of $\mathcal{G}$ in terms of
Congruences Between Abelian p-Adic Zeta Functions
This article is a reproduction of lectures in the workshop based on Sect. 6 of [Kak10] with a slight change in the notation to make it consistent with previous articles in the volume. Fix an odd

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In this paper, we will construct the p-adic zeta function for a non-commutative p-extension F of a totally real number field F such that the finite part of its Galois group G is a p-group with
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