The relative class number of certain imaginary abelian number fields of odd conductors (Q1924885)

It is a well known result due to \textit{L. Carlitz} and \textit{F. R. Olson} [Proc. Am. Math. Soc. 6, 265-269 (1955; Zbl 0065.02703)] that the Maillet determinant is a multiple of the minus class number of \(\mathbb{Q} (\zeta_p)\), and similar expressions are known for other abelian CM-fields. Recently, \textit{F. Hazama} [J. Number Theory 34, No. 2, 174-177 (1990; Zbl 0697.12003)] proved the same for the determinant of the Demyanenko matrix. In this paper, the author defines a Demyanenko matrix for composita \(K\) of \(\mathbb{Q} (\zeta_p)\) and quadratic number fields and shows that its determinant is the product of the minus class number of \(K\) and an explicitly given factor.