Reflection theorems and the p-Sylow subgroup of K2OF for a n

Abstract

Communicated by C.A. Weibel MSC: 11R37 11R29 19F15 a b s t r a c tFor any odd prime p, we present a reflection theorem which for p = 3 is the Scholz Reflection Theorem. We obtain some formulas for the p-rank and the p n -rank(K 2 O F ), where F is a number field. With the help of our reflection theorem, we establish relations between the p n -divisibility of the order of K 2 O F and the p n -divisibility of the class number of some algebraic number fields F .