On pj-rank of Even K-groups of Rings of Integers

Abstract

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 p^j-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 ℤ_l-extension, where l ≠ p.