Abstract
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( 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 .
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