Extensions with Galois group Hol(C8) unramified over a complex quadratic number field

Abstract

We study normal extensions with Galois group Hol($C_8$) that are unramified over a complex quadratic subfield. The Galois group is either the semi-dihedral group or the modular group of order $16$. We present an explicit construction of such fields.

arXiv comment17 pages