It is known that a (generalized) soluble group whose proper subgroups of infinite rank are abelian either is abelian or has finite rank. It is proved here that if is a group of infinite rank such that all its proper subgroups of infinite rank have locally finite commutator subgroup, then the commutator subgroup of is locally finite, provided that satisfies a suitable generalized solubility condition. Moreover, a similar result is obtained for groups whose proper subgroups of infinite rank are quasihamiltonian.
Cite this article
Maria De Falco, Francesco de Giovanni, Carmela Musella, Nadir Trabelsi, Groups with restrictions on subgroups of infinite rank. Rev. Mat. Iberoam. 30 (2014), no. 2, pp. 537–550