Determination of totally imaginary cyclic quartic fields with ideal class group of exponent \(\leq 2\) (Q1313300)

Let \(K\) be an imaginary cyclic quartic field. Let \(H(K)\) denote the ideal class group of \(K\), and let \(h(K)= \text{card } H(K)\). The author shows that there are precisely 33 fields \(K\) with exponent 1 or 2. It is the reviewer's opinion that the author fails to acknowledge sufficiently the work of previous authors in the area. For example, \textit{B. Setzer} [Math. Comput. 35, 1383-1386 (1980; Zbl 0455.12004)] has determined all such \(K\) with \(h(K)=1\). This is not mentioned. Neither is the determination of all such \(K\) with \(h(K)=2\) by \textit{K. Hardy}, \textit{R. H. Hudson}, \textit{D. Richman} and \textit{K. S. Williams} [Trans. Am. Math. Soc. 311, 1-55 (1989; Zbl 0678.12003)].