Polynomials over \({\mathbb{Q}}\) solving an embedding problem
The fields defined by the polynomials constructed by \textit{E. Nart} and the author in [J. Number Theory 16, 6-13 (1983; Zbl 0511.12010), Th. 2.1], with absolute Galois group the alternating group \(A_ n\), can be embedded in any central extension of \(A_ n\) if and only if \(n\equiv 0 (mod 8)\), or \(n\equiv 2 (mod 8)\) and n is a sum of two squares. Consequently, for theses values of n, every central extension of \(A_ n\) occurs as a Galois group over \({\mathbb{Q}}\).
embedding in central extension of \(A_ n\)
central extension of \(A_ n\) as Galois group
scientific article; zbMATH DE number 3869466