共查询到10条相似文献，搜索用时 46 毫秒
1.
In this article, we study the classification of flag‐transitive, point‐primitive 2‐ (v, k, 4) symmetric designs. We prove that if the socle of the automorphism group G of a flag‐transitive, point‐primitive nontrivial 2‐ (v, k, 4) symmetric design ?? is an alternating group An for n≥5, then (v, k) = (15, 8) and ?? is one of the following: (i) The points of ?? are those of the projective space PG(3, 2) and the blocks are the complements of the planes of PG(3, 2), G = A7 or A8, and the stabilizer Gx of a point x of ?? is L3(2) or AGL3(2), respectively. (ii) The points of ?? are the edges of the complete graph K6 and the blocks are the complete bipartite subgraphs K2, 4 of K6, G = A6 or S6, and Gx = S4 or S4 × Z2, respectively. © 2011 Wiley Periodicals, Inc. J Combin Designs 19:475‐483, 2011 相似文献
2.
In this article, we show that if is a nontrivial nonsymmetric design admitting a flag‐transitive point‐primitive automorphism group G, then G must be an affine or almost simple group. Moreover, if the socle of G is sporadic, then is the unique 2 ? (176, 8, 2) design with , the Higman–Sims simple group. 相似文献
3.
In this article, we study symmetric designs admitting a flag‐transitive and point‐primitive automorphism group whose socle is isomorphic to a projective special linear group of dimension at most four. We, in particular, determine all such possible parameters and show that such a design belongs to one of two infinite families of point‐hyperplane designs or it is isomorphic to a design with parameters (7, 3, 1), (7, 4, 2), (11, 5, 2), (11, 6, 3), (15, 8, 4), (35, 18, 9), or (56, 45, 18). 相似文献
4.
Nonsymmetric designs, with , admitting a solvable flag‐transitive automorphism group of affine type not contained in are classified. 相似文献
5.
It is shown that, if is a nontrivial 2‐ symmetric design, with , admitting a flag‐transitive automorphism group G of affine type, then , p an odd prime, and G is a point‐primitive, block‐primitive subgroup of . Moreover, acts flag‐transitively, point‐primitively on , and is isomorphic to the development of a difference set whose parameters and structure are also provided. 相似文献
6.
In this paper, we establish the existence of some infinite families of 2‐designs from ‐dimensional projective geometry , which admit ‐dimensional projective special linear group as their flag‐transitive automorphism group. 相似文献
7.
8.
By this article we conclude the construction of all primitive ( v, k,λ ) symmetric designs with v < 2500 , up to a few unsolved cases. Complementary to the designs with prime power number of points published previously, here we give 55 primitive symmetric designs with v ≠ p m , p prime and m positive integer, together with the analysis of their full automorphism groups. The research involves programming and wide‐range computations. We make use of the software package GAP and the library of primitive groups which it contains. © 2011 Wiley Periodicals, Inc. J Combin Designs 19:463‐474, 2011 相似文献
9.
设$D$是一个非平凡的对称$(v,k,lambda)$设计, $G$是$D$的一个自同构群.本文证明了如果$G$以二维典型群PSL$(2,q)$作为基柱且在$D$上的作用是旗传递和点本原的,那么设计$D$的参数只能为$(7, 3, 1)$, $(7, 4, 2)$, $(11, 5, 2)$, $(11, 6, 3)$或$(15, 8, 4)$. 相似文献
10.
The purpose of this paper is to classify all pairs , where is a nontrivial 2‐ design, and acts transitively on the set of blocks of and primitively on the set of points of with sporadic socle. We prove that there exists only one such pair : is the unique 2‐(176,8,2) design and , the Higman–Sims simple group. 相似文献