University of IsfahanInternational Journal of Group Theory2251-76503120140301Groups with minimax commutator subgroup916296810.22108/ijgt.2014.2968ENFrancescoDe GiovanniDipartimento di Matematica e Applicazioni - University of Napoli "Federico II"MarcoTrombettiDipartimento di Matematica e Applicazooni - University of Napoli "Federico II"0000-0003-4532-3690Journal Article20130430A 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