Abstract
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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
