\(K\)-groups and wreath products.
A group is called a \(K\)-group if its subgroup lattice is a complemented lattice. All finite simple groups are \(K\)-groups. On the other hand, the structure of finite soluble \(K\)-groups has been characterized by one of the authors long time ago, [\textit{G. Zacher}, Rend. Sem. Mat. Univ. Padova 22, 113-122 (1953; Zbl 0051.25802)]. However, in the general case there is no characterization of such groups. In the article under review, the authors give several criteria for a wreath product to be a \(K\)-group.
scientific article; zbMATH DE number 5147111