DIHEDRAL QUINTIC FIELDS WITH A POWER BASIS

Abstract

to be monogenic. Dummit and Kisilevsky[4] have shown that there exist infinitely many cyclic cubic fields whichare monogenic. The same has been shown for non-cyclic cubic fields, purequartic fields, bicyclic quartic fields, dihedral quartic fields by Spearman andWilliams [15], Funakura [6], Nakahara [14], Huard, Spearman and Williams[10] respectively. It is not known if there are infinitely many monogeniccyclic quartic fields. If