Soluble Groups Wıth The Mınımum Condıtıon For Normal Subgroups


Thesis Type: Postgraduate

Institution Of The Thesis: Gazi Üniversitesi, Fen Bilimleri Enstitüsü, Turkey

Approval Date: 2019

Student: HATİCE BÜŞRA ÖZBİNGÖL

Consultant: AYNUR ARIKAN

Abstract:

In this study, the article called Soluble groups with the minimum condition for normal subgroups by David McDougall was studied. In the article, the class of metabelian groups having no proper of a finite index and satisfying the minimum condition for normal subgroups have been studied. Groups with this structure are denoted by X. Main results in this study are given for this structure X. It is shown that the Sylow - subgroups of X groups are abelian for all primes . Using this result, it can be seen that an X group splits over its derived group and that the complements are conjugate. Group constructions which have similar structure have been given. Thus, basic results about soluble groups with the minimum condition for normal subgroups were obtained. In this thesis the Work of David Mc Dougall containing the above results are studied. The ideas and the methods used in the proofs are explained in detail and the gaps in the proofs are filled. Furthermore this work of David Mc Dougall has been made more understandable and proof of many properties have been provided.