Infınıtely Generated Groups Whose Proper Subgroups Are Solvable

---

Thesis Type: Postgraduate

Institution Of The Thesis: Gazi University, Turkey

Approval Date: 2016

Thesis Language: Turkish

Student: Oğuz Alkış

Supervisor: AYNUR ARIKAN

Abstract:

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.