On a problem of Hasse for certain imaginary Abelian fields (Q1864864)

The author considers the problem of monogeneity in certain composite fields. If \(K\) is the composite of an imaginary quadratic field \(M\) and a real Abelian field \(L\neq \mathbb{Q}\) whose conductors are coprime, then \(K\) is monogenic except if \(M=\mathbb{Q}(i)\). If \(K\) is sextic and \(M=\mathbb{Q}(i)\) then \(K\) is monogenic except for two fields of conductors 28 and 36. If \(K\) is the composite of \(M=\mathbb{Q}(i)\) and the maximal real subfield of a cyclotomic field of odd conductor \(f>1\), then \(K\) is monogenic. For some related results on power integral bases in composite fields see the reviewer's monograph [Diophantine equations and power integral bases. Boston: Birkhäuser (2002; Zbl 1016.11059)].