Steinberg triality groups acting on 2-(v,k,1)designs  

作　　者：刘伟俊 

机构地区：[1]Key Laboratory of Pure and Applied Mathematics, Institute of Mathematics, Peking University, Beijing 100871, China [2]Department of Mathematics, Railway Campus, Central South University, Changsha 410075, China

出　　处：《Science China Mathematics》2003年第6期872-883,共12页中国科学：数学（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant No.10171089).

摘　　要：A 2 - (υ, k, 1) design D = (?,?, ?) is a system consisting of a finite set ? of υ points and a collection ? of ?-subsets of ?, called blocks, such that each 2-subset of ? is contained in precisely one block. Let G be an automorphism group of a 2-(υ, 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 3 D 4(q). This paper is part of a project to classify groups and designs where the group acts primitively on the blocks of the design.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.

关 键 词：block-primitive  design  automorphism. 

分 类 号：O152[理学—数学]