Institution Of The Thesis: Gazi University, Turkey
Approval Date: 2016
Thesis Language: Turkish
Student: Oğuz Alkış
Consultant: AYNUR ARIKANAbstract:
In this thesis, the article written by A. O. Asar titled On infinitely generated groups whose proper subgroups are solvable is studied. In this work, infinitely generated groups whose proper subgroups are solvable and whose homomorphic images finitely generated subgroups having residually nilpotent normal closures have been studied. It is shown that a periodic group with this property is locally finite and either solvable or a locally nilpotent p-group having 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.