Groups with a maximality condition for some non-normal subgroups
Many authors have considered groups satisfying the minimal or the maximal condition on the set of subgroups which do not satisfy a property \(\mathcal P\). In particular [\textit{G. Cutolo}, Riv. Mat. Pura Appl. 9, 49-59 (1991; Zbl 0751.20022)] groups with the maximal condition on the set of non- normal subgroups are investigated, and this condition is equivalent to the maximal condition on the set of finitely generated non-normal subgroups. In this article the authors consider groups satisfying the maximal condition on the set of non-normal subgroups which are not finitely generated. The main theorem of the paper concerns the classification of generalized soluble groups with this property. As a corollary a description is obtained of generalized soluble groups in which every non-normal subgroup is finitely generated. The special case of nilpotent groups with this property was already considered in the above quoted paper by Cutolo.
maximal condition on sets of nonnormal subgroups
finitely generated non- normal subgroups
scientific article; zbMATH DE number 806236
scientific article