A remark on quaternion extensions of the rational p-adic field
Let F be a rational p-adic field \({\mathbb{Q}}_ p\). There exists a Galois quaternion extension of \(F={\mathbb{Q}}_ p\) if and only if \(p\equiv 3 mod 4\) or \(p=2\). There are introduced all quaternion extensions of \({\mathbb{Q}}_ p\) in a fixed algebraic closure of \({\mathbb{Q}}_ p\).
scientific article; zbMATH DE number 4210281