Groups whose proper subgroups are locally finite-by-nilpotent

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Thesis Type: Postgraduate

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

Approval Date: 2012

Thesis Language: Turkish

Student: Sevilay Akyol

Supervisor: AYNUR ARIKAN

Abstract:

In this thesis the paper written by Abel Dilmi titled Groups whose proper subgroups are locally finite-by-nilpotent is studied. In this paper minimal non (LF)Ngroups are looked into. First of all, to prove a few theorems in this thesis we considered the paper titled On torsion-by-nilpotent groups written by Endimioni and Troustason. In the third chapter of this thesis, the theorem is proved that is similar to P.Hall's best known corollary Let H be a normal subgroup of a group G. If H and G/H¢ are (LF)N group then G is (LF)N group and in the fourth chapter, the theorem is proved that's given in Amel Dilmi's article If G is a minimal non (LF)Ngroup, then G is a finitely generated perfect group which has no non-trivial finite factor and such that G/FratG is an infinite simple group in detail. It is given in detail that the proofs that are made for minimal non (LF)Ngroups are also valid for minimal non (LF) c N -groups. Thus in this paper Amel Dilmi's article is put into more clear, detailed and easily understandable form.