Document Details Document Type : Thesis  Document Title : Finites transitive groups of rank 3 الزمر الانتقالية من الرتبة الثالثة   Subject : Mathematics  Document Language : Arabic  Abstract : In this thesis, rank 3 groups are studied combinatorial and in a systematic way. The first chapter is introductory, and gives some basic definitions, terminology and preliminary concepts. In Chapter 2, we study the relationship between rank 3 groups and strongly regular graphs. We also give a necessary and sufficient condition for a group G to be primitive. Finally in section 3, ~provide basic facts and parameters used in theoretical and computational work on rank 3 groups. In Cliapter 3, we discuss five families of parameters of rank 3 graphs and their corresponding automorphism groups of rank 3. In the last section, we investigate an important class of rank 3 graphs with no triangles. In Section 1 of Chapter 4, we prove that the existence of a balanced incomplete block design implies the existence of a strongly regular graph with certain parameters. In section 2, we give a new proof for the existence of a rank 3 graph having parameters (18,9,9) and find its corresponding rank 3 group. In Section 3 , we prove the existence of a new rank .. 3 graph with parameters (25,8,4) and find its corresponding rank 3 group. In the fourth and final section of this Chapter, we discuss a new family of rank 3 graphs. We prove its feasibility for all integers m ~ 2. But rer\.1izability is established only for m = 2, as the classical simple group P Sp( 4,3) of order 25,920 is the corresponding rank 3 group in this case. In Chapter 5, we give a classification of finite primitive permutation groups of rank 3 by determining the groups in which the socle L of G is a sporadic simple group. In Section 1, we make a complete table of all such 19 sporadic simple groups of rank 3. In Section 2, we study, in great detail, the historical Higman- Sims sporadic simple group of rank 3 of order 44,352,000 [21]. In the third and last section we discuss briefly the first nine sporadic I simple groups of rank 3  Supervisor : Dr. Saeed Ahmad Shad  Thesis Type : Master Thesis  Publishing Year : 1415 AH 1994 AD  Co-Supervisor : Prof. Hamza Ali Abujabal  Added Date : Wednesday, June 11, 2008  Researchers Researcher Name (Arabic) Researcher Name (English) Researcher Type Dr Grade Email أحمد ناصر الصلبي Asslbi, Ahmed Nasser Researcher Master   Files File Name Type Description  23466.pdf pdf Abstract  23467.pdf pdf المستخلص Back To Researches Page