University of Isfahan International Journal of Group Theory 2251-7650 3 1 2014 03 01 Groups with minimax commutator subgroup 9 16 2968 10.22108/ijgt.2014.2968 EN Francesco De Giovanni Dipartimento di Matematica e Applicazioni - University of Napoli "Federico II" Marco Trombetti Dipartimento di Matematica e Applicazooni - University of Napoli "Federico II" Journal Article 2013 04 30 A result of Dixon‎, ‎Evans and Smith shows that if $G$ is a locally (soluble-by-finite) group whose proper subgroups are (finite rank)-by-abelian‎, ‎then $G$ itself has this property‎, ‎i.e‎. ‎the commutator subgroup of $G$ has finite rank‎. ‎It is proved here that if $G$ is a locally (soluble-by-finite) group whose proper subgroups have minimax commutator subgroup‎, ‎then also the commutator subgroup $G'$ of $G$ is minimax‎. ‎A corresponding result is proved for groups in which the commutator subgroup of every proper subgroup has finite torsion-free rank.‎ https://ijgt.ui.ac.ir/article_2968_a0361dfd4b08b2933ad65f68ad95fcd2.pdf