The structure of the 2-Sylow-subgroup ofK 2(α), I

Elements of order 4 of the Hilbert kernel in quadratic number fields

“…We use the method of [5,9] to investigate the elements of order 4 of K 2 O F for quadratic fields F . Now, we describe the notations of [5]:…”

“…Then ker χ is determined by the elements of order 4 of K 2 O F and the elements a ∈ F * with {−1, a} = 1 (see [5], Prop. 2.3, or [9], Prop. 1.5).…”

“…In the present paper, we concentrate on the structure of the 2-Sylow subgroup of K 2 O F and use the method of [5,9] to give the results of [12,13,14] and to express the forms of elements of order 4 of K 2 O F for quadratic fields F , which are simpler. Using these forms we discuss whether elements of order 4 of K 2 O F are contained in Hilbert kernel 2 F .…”

On two-primary algebraic K-theory of quadratic number rings with focus on K₂

“…It follows from Theorem 2.9 that δ equals 0 if d ∈ M −1 ∪ M −2 and 1 in all all other cases. Various 4-rank formulas for K 2 are known, see [5] and [9]. We will use the following results from [1].…”

The 4-rank of $K₂O_F$ for real quadratic fields F

“…Let F be a number field, and let O F be the ring of its integers. Several formulas for the 4-rank of K 2 O F are known (see [7], [5], etc.). If √ −1 ∈ F , then such formulas are related to S-ideal class groups of F and F ( √ −1), and the numbers of dyadic places in F and F ( √ −1), where S is the set of infinite dyadic places of F .…”