Groups whose non-normal subgroups have small commutator subgroup - De Falco, M.; de Giovanni, F.; Musella, C. (Algebra and Discrete Mathematics, 2007)
The structure of groups whose non-normal subgroups have a finite commutator subgroup is investigated. In particular, it is proved that if k is a positive integer and G is a locally graded group in which every non-normal subgroup has finite commutator subgroup of order at most k, then the commutator subgroup of G is finite. Moreover, groups with finitely many normalizers of subgroups with large commutator subgroup are studied.