Groups whose proper subgroups are locally finite-by-nilpotent

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)N?groups 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 iis proved that is similar to P.Hall?s best known corollary ? Let H be a normal subgroup of a group G. If H and 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)N?group, 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)N?groups are also valid for minimal non (LF) -groups. Thus in this paper Amel Dilmi?s article is put into more clear, detailed and easily understandable form.Key Words : nilpotent group, locally finite group, torsion group