Some results related with the subgroups of the extended Hecke group H ̅(λ_5)

In this thesis, some results are given fort he the extended Hecke group 𝐻 ̅ 5. The thesis consists of four sections. In the first section of the thesis, the definition of the extended Hecke group 𝐻̅5 is given and a general introduction of the thesis is made. In the second section of the thesis, definitions, theorems and methods belonging to the topics to be studied or used in the thesis are given. In the third section of the thesis, the subgroup 𝐻5𝛼, which is one of the 2-index subgroups of the extended Hecke group 𝐻 ̅ 5, is studied. Some of the subgroups of the group 𝐻 ̅ 5 (power, commutator and the commutator subgroups of the power) have been studied. In addition, it is shown that the images of these subgroups under the α automorphism are equal to similar subgroups of the Hecke group 𝐻5. In the fourth section of the thesis, the obtained results are given and suggestions are made for future studies.