Locally (soluble-by-finite) groups with all proper non-nilpotent subgroups of finite rank
The authors consider the intersection of the class mentioned in the title with classes \(N^*_c\) and \((A^2)^*\), where the star means every proper non-\(N_c\) (non-\(A^2\)) subgroup has finite rank. Example (Theorem A): Let \(G\) be a locally (soluble-by-finite) group in the class \(N^*_c\) for some positive integer \(c\). Then either \(G\in N_c\) or \(G\) has finite rank. Further interesting results are found on conjunctions with the closure with respect to local systems, sub-Cartesian products, ascending and descending normal series of the class of locally graded periodic groups.
scientific article; zbMATH DE number 1308299
scientific article