Abstract algebra and numbers theory with GAP (Group, algorithm and programming)

ABSTRACT ALGEBRA AND NUMBERS THEORY WITH GAP (GROUP, ALGORITHM AND PROGRAMMING) Alper ODABAŞ Mathematics, MSc Thesis, 2004 Thesis Adviser: Assoc. Prof. Dr. Murat ALP SUMMARY This thesis consists of eighteen chapters. In the first chapter, the introduction was given. Getting GAP (Group, Algorithm and Programming) program, downloading it from internet and installing it to the Windows operation systems were placed in the second chapter. In the third chapter, a short presentation of GAP program commands were given. Using the GAP functions was presented in the fourth chapter with their examples. The other chapters were set apart for the subjects of algebra and examples of each subject. Bölüm 5, kümeler ve kümelerle ilgili örnekleri içermektedir. Bölüm 6, fonksiyonlar ve fonksiyon kavramıyla ilintili olan bilgilerin GAP programı aracılığı ile sunulmasını içermektedir. In chapter 5, sets and examples were explained. Functions and presentation of informations about functions through GAP program were located in chapter 6. In chapter 7, integers, greatest common divisor, least common multiple were given. Modular arithmetic and its GAP application were presented in chapter 8. Group theory, and investigation of this concept by using GAP program were presented in chapter 9. In chapter 10, subgroups and their examples were explained. Normal subgroups and investigation of this subject by using GAP were located in chapter 1 1. Subgroups and their examples were given in chapter 12. In chapter 13, symmetric groups and examples concerned with them were presented. In chapter 14, Sylow theorems were explained. Rings, subrings, ideals and their examples were located in chapter 15. Integral domain, fields, subfields and investigation of these consepts by using GAP program were given in chapter 16. Division ring homomorphisms and their GAP program examples were explained in chapter 1 7. Finally, in chapter 18, group lattices were presented. Keywords : GAP, Group, Group Homomorphism, Group Lattice, Integers, Integer Domain, Modular Arithmetic, Normal Subgroup, Subgroup, Subfield, Subring, Sylow Theorem, Symmetric Group.