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 pn-rank(K2OF), where F is a number field. With the help of our reflection theorem, we establish relations between the pn-divisibility of the order of K2OF and the pn-divisibility of the class number of some algebraic number fields F.