Ideal class groups of exponent two and one-class genera of binary quadratic lattices (Q915764)

Let \(K/K_ 0\) be a relative quadratic extension of algebraic number fields with rings R resp. \(R_ 0\) of algebraic integers. The relationship between the following two statements is considered: 1) R has genus class number one as quadratic \(R_ 0\)-lattice. 2) All squares in the ideal class group of K are trivial. In the case K imaginary quadratic field and \(K_ 0={\mathbb{Q}}\), the statements are equivalent. In general certain partial results, especially for CM-fields, concerning the relation of 1) with 2) are proved.