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引用次数: 0
摘要
设 L/F 是 n 阶数域的有限伽罗瓦扩展，设 p 是不除以 n 的素数。我们将按照岩泽（Iwasawa）和小松中野（Komatsu-Nakano）的方法，通过伽罗瓦模块结构来研究 \(K_{2i}(\mathcal{O}_{L})\的 pj-rank。在此过程中，我们将 Browkin、Wu 和 Zhou 以前对 K2 群的观察推广到更高的偶数 K 群。我们还举例说明了我们的结果。最后，我们运用我们的讨论来完善北岛（Kitajima）关于偶数 K 群在环ℤl-扩展（其中 l ≠ p）中的 p 级的结果。
Let L/F be a finite Galois extension of number fields of degree n and let p be a prime which does not divide n. We shall study the pj-rank of \(K_{2i}(\mathcal{O}_{L})\) via its Galois module structure following the approaches of Iwasawa and Komatsu–Nakano. Along the way, we generalize previous observations of Browkin, Wu and Zhou on K2-groups to higher even K-groups. We also give examples to illustrate our results. Finally, we apply our discussion to refine a result of Kitajima pertaining to the p-rank of even K-groups in the cyclotomic ℤl-extension, where l ≠ p.
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