Groups of infinite rank with a locally finite term in the lower central series.
A group \(G\) is called strongly locally graded, if every finitely generated nontrivial subgroup of any quotient group \(H/K\) contains a proper subgroup of finite index. The authors prove: If \(G\) is a strongly locally graded group of infinite rank and all proper subgroups of infinite rank of \(G\) are (locally finite)-by-nilpotent [(locally finite)-by-(locally nilpotent)], then so is \(G\) itself. (So here subgroups of finite rank need not be considered.)
(locally finite)-by-(locally nilpotent) groups
scientific article; zbMATH DE number 6495597