Thompson'ın grupları üzerine

In this thesis, we tried to explain the properties of Thompson's T group and its relationship with the tree we created with the group effect on the upper-half plane through continued fractions. Thompson's T group is a finitely generated simple infinite group. We can achieve this group with the help of fractional linear transformations obtained by applying the movement we define as flip movement on the tree we created with continued fractions. In this study, continued fractions and fractional linear transformations were discussed. Thompson's T group was tried to be obtained with the help of the Modular group using the group effect. This thesis is composed of three chapters. In the first chapter, Thompson's T group is introduced, and its relationship with the modular group is examined. In the second chapter, group cohomology was examined by introducing the concepts of homology and cohomology. In the last chapter, it is given how the group cohomology, which is introduced in the second chapter, is obtained with the help of group extensions, and we proposed a conjecture concerning the second cohomology of Thompson's group T.