%0 Journal Article
%T Groups with minimax commutator subgroup
%J International Journal of Group Theory
%I University of Isfahan
%Z 2251-7650
%A de Giovanni, Francesco
%A Trombetti, Marco
%D 2014
%\ 03/01/2014
%V 3
%N 1
%P 9-16
%! Groups with minimax commutator subgroup
%K minimax group
%K commutator subgroup
%K torsion-free rank
%R 10.22108/ijgt.2014.2968
%X 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.
%U https://ijgt.ui.ac.ir/article_2968_a0361dfd4b08b2933ad65f68ad95fcd2.pdf