Finite \(p\)-groups with cyclic commutator subgroup and cyclic center
The author classifies the finite \(p\)-groups with cyclic commutator subgroup and cyclic center; for \(p=2\) the condition \([G',G]\subseteq G^{\prime 4}\) is added. It turns out that there are 13 types of such groups when its class \(c(G)\) is greater than 2 (the case \(c(G)=2\) has been settled already by \textit{Y. K. Leong} [J. Aust. Math. Soc., Ser. A 17, 142-153 (1974; Zbl 0286.20022) and 27, 125-140 (1978; Zbl 0402.20018), respectively]). Also all possible cases, when isomorphic groups occur, are listed.
scientific article; zbMATH DE number 1262489