Tez özetleri Astronomi ve Uzay Bilimleri Anabilim Dalı 2

Cowlex Characters Of Fmte Groups

Character theory is an important tool for studying finite groups and their representations. The first studies in this area belong to F. G. Frobenius. W. Burnside's book , Theory of Groups of Finite Order, published in 1911, is the first book to give a systematic account of representation theory. This book contains many results on abstract groups proved by using group characters. In this thesis, we have attempted to provide an introduction to the complex character theory of finite groups. During the preparation of the thesis, it was significantly benefited from I. Martin Isaacs' book Character Theory of Finite Groups. The basic definitions and fundamental theorems of character theory are given in Chapter 2. Chapter 3 is concerned with the representations and complex characters of a finite group. Orthogonality relations and character table properties are given here. In this chapter, it is also explained that how information about a finite group can be recovered from its character table. Bumside•s theorem, an important theorem in group theory, is stated and proved in Chapter 4. Induced characters are main concem of Chapter 5. Clifford-s theorem and Taketa' s theorem are given in this chapter. Brauer's lemma on character tables is given in Chapter 6 to determine the irreducible characters of Frobenius groups. Moreover, in Chapters 7 and 8, the character tables of dihedral groups are constructed and a useful method for constructing character tables of symmetric groups is presented. Finally, an introduction to character degree graphs is given and corresponding character degree graphs for symmetric and altemating groups are presented in the thesis.