On a reduction theorem for finite, bipartite 2-arc-transitive graphs
On a reduction theorem for finite, bipartite 2-arc-transitive graphs
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发表时间：
1993
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通讯作者：
C. Praeger
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作者：
C. Praeger
设r为有限连通正则二部2-弧传递图。证明了r是一个可能更小的图E的覆盖，它也是与r同价的连通正则图，并且存在Aut:E的一个子群G，使得G在E上是2弧可传递的，并且G的每个非平凡法向子群在顶点上最多有两个轨道。研究了这样的图：E，其中子群G有一个带两个轨道的阿贝尔正规子群。证明了E是一个2弧传递的Cayley图，对于(a)初等阿贝尔2-群，或(b)群，其中N是奇数阶的初等阿贝尔群，T是2阶的元素，反转N的每一个元素。
Let r be a finite connecied regular bipartite 2-arc transitive graph. It is shown that r is a cover of a possibly smaller graph :E, which is also connecied and regular of the same valency as r, and there is a subgroup G of Aut :E such that G is 2-arc transitive on :E and every nontrivial normal subgroup of G has at most two orbits on vertices. Such graphs :E for which the subgroup G has an abelian normal subgroup with two orbits are investigated. It is shown that :E is a 2-arc transitive Cayley graph for either (a) an elementary abelian 2-group, or (b) a group , where N is an elementary abelian group of odd order and T, an element of order 2, inverts every element of N. The graphs :E arising in (a) have been classified recently by A.A. Ivanov and the author.