We explicitly calculate all the 2-primary higher algebraic K-groups of the rings of integers of all 2-regular quadratic number fields, cyclotomic number fields, or maximal real subfields of such. Here 2-regular means that (2) does not split in the number field, and its narrow Picard group is of odd order. Mathematics Subject Classification (1991): 19D50, 11R11, 11R18, 11R37, 11R42,19F27. [References: 15]
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