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- W4385714013 abstract "Let $k$ be a given positive odd integer and $p$ an odd prime. In this paper, we shall give a sufficient condition when a prime $p$ divides the order of the groups $K_{2k}(mathbb{Z}[zeta_m+zeta_m^{-1}])$ and $K_{2k}(mathbb{Z}[zeta_m])$, where $zeta_m$ is a primitive $m$th root of unity. When $F$ is a $p$-extension contained in $mathbb{Q}(zeta_l)$ for some prime $l$, we also establish a necessary and sufficient condition for the order of $K_{2(p-2)}(mathcal{O}_F)$ to be divisible by $p$. This generalizes a previous result of Browkin which in turn has applications towards establishing the existence of infinitely many cyclic extensions of degree $p$ which are $(p, p-1)$-rational." @default.
- W4385714013 created "2023-08-10" @default.
- W4385714013 creator A5071526289 @default.
- W4385714013 date "2023-08-08" @default.
- W4385714013 modified "2023-09-27" @default.
- W4385714013 title "On the $p$-divisibility of even $K$-groups of the ring of integers of a cyclotomic field" @default.
- W4385714013 doi "https://doi.org/10.48550/arxiv.2308.04099" @default.
- W4385714013 hasPublicationYear "2023" @default.
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