On infinitely generated groups whose proper subgroups are solvable

In this work infinitely generated groups are considered whose proper subgroups are solvable and in whose homomorphic images finitely generated subgroups have residually nilpotent normal closures. It is shown that a periodic group with this property is locally finite and either solvable or is a locally nilpotent p-group and has a homomorphic image which is a perfect Fitting group with additional properties. However if “residually nilpotent” is replaced by “residually (finite and nilpotent)”, then the group is solvable. Furthermore if G is non-periodic and locally nilpotent, then the group is solvable without the hypothesis on normal closures.