Groups and geometries

In group theory, there have been many studies on finite groups. One of important studies is geometric examination of all finite and simple groups. In this thesis, finite groups and geometries are studied. This thesis consists of six chapters. In the first part, studies of abstract algebra are given. Some basic information used in this thesis is presented in the second part. In the third part, projective special linear groups are defined and properties related to them are given. In the fourth chapter, definations and propositions of incidence and coset geometries are given. In the fifth section, two methods are given that are used to obtain a new geometry of a finite known geometry. In the last section, using one of these methods, a new geomety is obtained from rank-5 geometry of the group M23.