Fintte two-arc transitive graphs admitting a suzuki simple group
Fintte two-arc transitive graphs admitting a suzuki simple group
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DOI：
10.1080/00927879908826659
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发表时间：
1999
影响因子：
0.7
通讯作者：
X. Fang;C. Praeger
中科院分区：
文献类型：
--
作者：
X. Fang;C. Praeger
本文是Firite拟本原2-弧传递图分类程序的一部分。文[9]证明了非二部2-弧传递图是拟本原2-弧传递图的覆盖，拟本原2-弧传递图可分为仿射型、几乎单纯型、乘积型和扭环型。这里Xe考虑一类几乎简单类型的图，即那些具有自同构群的图属于称为Suzulti群的几乎单群的不定族。设r是一个有限简单无向图，即r由一个有限顶点集L‘r和一个边集Er组成，这两个边集可以用来自IT的一个无序偶的子集来标识。2-URC是一个三元组(ao.N1，az)的顶点，使得{Ao，All，{al，a2)Eer和a“f a？设G是r的Anton~同构群Autr的一个子群，如果G在r的2-弧集上传递，则称图r为(G，2)-弧格；如果图r是(Autr.2)-弧传递的，则称r为2-urc变换.类似地，如果G在r的1-弧上传递，即在序偶(a0，al)上传递，则称r是(G，1)-czrc trunsitiue，其中{no，al)E et.集合R上的置换群G称为拟本原，如果G的每个非平凡正规子群在Q上传递，(G，2)-弧传递图称为拟本原(G，2)-弧传递图，如果G在R上拟本原.仿射型拟本原2-弧传递图已被Ivanov和第二作者[；I，Baddeley]完全分类
This paper forms part of a program for classifying fi~ lite quasiprimitive 2-arc transitive graphs. In [9] it xas shown that every non-bipartite 2-arc transitive graph is a cover of a quasiprimitive 2-arc transitive graph, and that the quasiprimitive 2-arc transitive graphs may be divided into those of affine type, of almost simple type, of product type, and of twisted wreath type. Here xe consider a family of such graphs of almost simple type namely those with autoinorphisni group belonging to the illfinite family of almost simple groups called the Suzulti groups. Let r be a finite simple undirected graph, that is r consists of a finite vertex set l'r and an edge set Er which may be identified with a subset of unordered pairs from IT. A 2-urc is a triple (ao. nl, az) of vertices such that {ao, all,{al, a2) E Er and a" f a?. Let G be a subgroup of the anton~ orphism group Aut r of r. The graph r is said to be (G, 2)-arc trcmsitice if G is transitive on the set of 2-arcs of r; also r is said to be 2-urc trcznsiticeif it is (Aut r. 2)-arc transitive. Similarly r is said to be (G, 1)-czrc trunsitiue if G is transitive on the 1-arcs of r, that is, on the ordered pairs (ao, al) where {no, al) E ET. A permutation group G on a set R is said to be qucisiprimitive if every nontrivial normal subgroup of G is transitive on Q, and a (G, 2)-arc transitive graph is said to be a quasiprimitice (G, 2)-arc trnnsiti~ 3e graph if G is quasiprimitive on\; r. The quasiprimitive 2-arc transitive graphs of affine type have beein completely classified by Ivanov and the second author in [; I, and Baddeley