| Steinberg triality groups acting on 2 - (v, k, 1) designs |
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| 引用本文： | 刘伟俊. Steinberg triality groups acting on 2 - (v, k, 1) designs[J]. 中国科学A辑(英文版), 2003, 46(6) |
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| 作者姓名： | 刘伟俊 |
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| 作者单位： | Key Laboratory |
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| 摘 要： | A 2 - (v,k,1) design D = (P, B) is a system consisting of a finite set P of v points and a collection B of k-subsets of P, called blocks, such that each 2-subset of P is contained in precisely one block. Let G be an automorphism group of a 2- (v,k,1) design. Delandtsheer proved that if G is block-primitive and D is not a projective plane, then G is almost simple, that is, T ≤ G ≤ Aut(T), where T is a non-abelian simple group. In this paper, we prove that T is not isomorphic to 3D4(q). This paper is part of a project to classify groups and designs where the group acts primitively on the blocks of the design.
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Steinberg triality groups acting on 2-(v,k,1) designs |
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| LIU WeijunKey Laboratory of Pure and Applied Mathematics. Steinberg triality groups acting on 2-(v,k,1) designs[J]. Science in China(Mathematics), 2003, 46(6) |
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| Authors: | LIU WeijunKey Laboratory of Pure and Applied Mathematics |
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| Affiliation: | Key Laboratory of Pure and Applied Mathematics, Institute of Mathematics, Peking University, Beijing 100871,China;Department of Mathematics, Railway Campus, Central South University, Changsha 410075, China |
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| Abstract: | A 2 - (v, k, 1) design D = (P,B) is a system consisting of a finite set P of v points and a collection B of k-subsets of P, called blocks, such that each 2-subset of P is contained in precisely one block.Let G be an automorphism group of a 2 - (v, k, 1) design. Delandtsheer proved that if G is block-primitive and D is not a projective plane, then G is almost simple, that is, T ≤ G ≤ Aut(T), where T is a non-abelian simple group. In this paper, we prove that T is not isomorphic to 3D4(q). This paper is part of a project to classify groups and designs where the group acts primitively on the blocks of the design. |
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| Keywords: | block-primitive design automorphism. |
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