\(K\)-groups and \(\lambda\)-invariants of algebraic number fields
Let \(F\) be a totally real number field and \(p\neq 2\) a prime. Let \(F'\) be a Galois \(p\)-extension of \(F\). Then the author gives sufficient conditions for the \(p\)-divisibility of \(| K_{2n}(O_{F'})|\) for \(n\) odd (essentially ramification conditions in the extension \(F'_{\infty}/F_{\infty}\) built with cyclotomic \(\mathbb Z_ p\)-extensions of \(F\), \(F'\)). The author uses Iwasawa's theory via a result of Galois descent of \textit{C. Soulé} [Invent. Math. 55, 251--295 (1979; Zbl 0437.12008)] and supposes that the \(\mu\)-invariant of \(F(\exp(2i\pi/p))\) is zero. Remark. The point (4) of the main theorem \((n=1)\) is now known in full generality by means of the concept of primitive ramification and regular fields [see the bibliography in \textit{G. Gras} and \textit{J.-F. Jaulent}, Math. Z. 202, No. 3, 343--365 (1989; Zbl 0704.11040)].
scientific article; zbMATH DE number 4146061