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Almost simple group with Si Tannuo 4 - Design

Author: LiaoXiaoLian
Tutor: LiuWeiJun
School: Central South University
Course: Basic mathematics
Keywords: Almost simple group Design Flag a pass Automorphism group Pillar
CLC: O152
Type: Master's thesis
Year: 2006
Downloads: 22
Quote: 1
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Abstract


In group theory and design theory study, the design of the automorphism group of the research could help us find a new design , in turn , will be designed from the same group as the automorphism group and can help us better understand some of the group structures. Therefore, the use of the classification theorem of finite simple groups are classified on the design , has become the field of algebra and combinatorics topics at the forefront . This paper will examine the Si Tannuo 4 - Design automorphism group is flag - transfer case is Si Tannuo 4 - Design automorphism group is the flag - the classification of the situation to pass part of the work . First, we introduced the theory of group theory and design history and current status of research and some related knowledge -based papers to establish the basic theoretical system ; secondly , in the third and fourth chapter , we introduce the Mathieu group , almost single- group in nature and introduces some important concepts and lemma , and were proved almost simple groups acting on Si Tannuo 4 - design two main theorem . Namely : the main Theorem 1 Let D = (X, B, I) is nontrivial Si Tannuo 4 - Design , D the automorphism group G flags - acts transitively on D . If G is almost simple group , then Soc (G) isomorphic to Suzuki group Sz (q) and the Ree group Re (q). Main Theorem 2 Let D = (X, B, I) is nontrivial Si Tannuo 4 - Design , D the automorphism group G flags - acts transitively on D . If G is almost simple group , then ⅰ) Soc (G) isomorphic to the following simple groups : ( 1 ) . N = PSL (2,11), v = 11; (2). N = PSL (2,8), v = 8; (3). N = M v , v = 12,22,24; (4). N = M 11 , v = 12; (5). N = A 4 , v = 15; (6). HS, v = 176; (7). CO 3 , v = 276; (8). N = A v , v ≥ 5. Ⅱ) If N = M 11 , v = 11, then D is a Si Tannuo 4 - ( 11,5,1 ) design, and G (?) M 11 . Ⅱ) If N = M 23 , v = 23, then D is a Si Tannuo 4 - ( 23,7,1 ) design, and G (?) M 23 .

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Group theory
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