Note on the Rank of 2-Class Group of \(\mathbb {Q}(i,\sqrt{p}, \sqrt{d})\)
摘要
Let \(p\equiv 5\pmod 8\) be a prime number and d any positive square-free integer. The main goal of this note is to give explicitly the 2-rank of the class group of the imaginary triquadratic number fields \(\mathbb {K}=\mathbb {Q}(i,\sqrt{p}, \sqrt{d})\) .