The exponent three class group problem for some real cyclic cubic number fields (Q2758969)

The cubic field \(K\) generated by a root \(\alpha\) of \(x^3 - mx^2 - (m+3)x - 1\) is called a simplest cubic field if \(\mathbb Z[\alpha]\) is the maximal order in \(K\). By improving estimates given by \textit{G. Lettl} [Math. Comput. 46, 659-666 (1986; Zbl 0602.12001)], the author shows that there are \(23\) such fields whose ideal class groups have exponent \(3\), the largest one occurring for \(m = 104\). He also shows that there are exactly \(5\) simplest cubic fields whose class groups have exponent \(2\), namely those with \(m = 11\), \(17\), \(23\), \(25\), and \(29\).