On some groups whose subnormal subgroups are contranormal-free
\textit{J. S. Rose} [Math. Z. 106, 97--112 (1968; Zbl 0169.03402)] introduced the concept of contranormal subgroups. These are defined as subgroups whose normal closure is the entire group. In this interesting article, the authors explore groups which have no contranormal subgroups, referring to them as ``contranormal-free''. Clearly, a finite group is nilpotent if and only if it is contranormal-free. The authors here study the infinite groups whose subnormal subgroups are contranormal-free groups, presenting many interesting and technical results, some of which describe the Baer groups. For example, they prove the following as a corollary of their main results:\N\NLet \(G\) be a periodic solvable group. If every subnormal subgroup of \(G\) is contranormal-free, then \(G\) is a Baer group.
upper central series, Baer group, contranormal-free groups
scientific article; zbMATH DE number 7927533