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.
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de Giovanni, F., & Trombetti, M. (2014). Groups with minimax commutator subgroup. International Journal of Group Theory, 3(1), 9-16. doi: 10.22108/ijgt.2014.2968
MLA
Francesco de Giovanni; Marco Trombetti. "Groups with minimax commutator subgroup". International Journal of Group Theory, 3, 1, 2014, 9-16. doi: 10.22108/ijgt.2014.2968
HARVARD
de Giovanni, F., Trombetti, M. (2014). 'Groups with minimax commutator subgroup', International Journal of Group Theory, 3(1), pp. 9-16. doi: 10.22108/ijgt.2014.2968
VANCOUVER
de Giovanni, F., Trombetti, M. Groups with minimax commutator subgroup. International Journal of Group Theory, 2014; 3(1): 9-16. doi: 10.22108/ijgt.2014.2968
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