Geodesic
Groups whose non-normal subgroups have small commutator subgroup
Algebra and discrete mathematics, no. 3 (2007), pp. 46-58.

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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.
Keywords: normal subgroup, commutator subgroup. 
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     author = {M. De Falco and F. de Giovanni and C. Musella},
     title = {Groups whose non-normal subgroups have small commutator subgroup},
     journal = {Algebra and discrete mathematics},
     pages = {46--58},
     publisher = {mathdoc},
     number = {3},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2007_3_a6/}
}
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M. De Falco; F. de Giovanni; C. Musella. Groups whose non-normal subgroups have small commutator subgroup. Algebra and discrete mathematics, no. 3 (2007), pp. 46-58. http://geodesic.mathdoc.fr/item/ADM_2007_3_a6/