Reflection theorems and the p-Sylow subgroup of K2OF for a number field F

For 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(K2OF), 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 K2OF and the p(n)-divisibility of the class number of some algebraic number fields F. (C) 2009 Elsevier B.V. All rights reserved.