2-Sylow Subgroups of K_2O_F for Real Quadratic Field and Class Group for Imaginary Quadratic Field

摘要

In this paper, we study the relation between the 2-Sylow subgroups of K_2O_F for real quadratic field F=Q(/d) and the class group C(E) for imaginary quadratic field E= Q(/-d). For general number field F, many authors have characterized the 2-Sylow subgroup Structure of K_2O_f an obtained 2~n-rank K_2O_F formulas (n<=1). Especially, for quadratic Field F, Qin Huorong~[1] got the formulas of 4-order elements in K_2O_F on the basis of Browkin-Schinzel~[1]. In this paper, we discuss them further.