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The term (di)graph is employed to mean that a graph in question is either a directed graph or an undirected graph.The symbol G(p,r)represents the digraph defined by Chao: V(G(p,r))=Zp,E(G(p,r))={(x,y)|x-y∈Hr},where P is a prime,r is a positive divisor of P-1 and Hr is the unique subgroup of order r in Aut(Zp).A Cayley graph (?)=Cay(G,S)is called imprimitive if A=Aut((?))acts imprimitively on V((?)).Let (?)=Cay(G,S)be a connected imprimitive arc-transitive graph on G=Z×Z,B={B0,B1,…,Bp-1}the complete block system of A=Aut((?))on V((?))=G and K the kernel of A on B.Then obviously K≠1. 相似文献
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§1.引 言 有限p-群作为有限群论的一个多少是独立的分支,近半个世纪以来,特别是近二十年来,有了很大的进步.虽然它的发展不象有限单群那样引人注目,在这个领域里工作的数学家人数也不多,但是近年来它的进展是不可忽视的.我们仅举出下列比较突出的工作为例:1958年,肯定回答了方次数为p的局限 Burnside问题;1965年,G.E.Wall对p=5的情形用反例否定了Hughes猜想;1966年,W.Gaschutz证明了有限非交换p-群具 相似文献
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图X称为边正则图,若X的自同构群Aut(X)在X的边集上的作用是正则的.本文考察了三度边正则图与四度Cayley图的关系,给出了一个由四度Cayley图构造三度边正则图的方法,并且构造了边正则图的三个无限族. 相似文献
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Let г be a connected undirected graph aud G a group of automorphisms ofг.G is said to act symmetrically on г and г is said to be G-symmetric, if G istransitive on the set {(α,β) |α,β adjacent vertices} of 1-arcs of г. Thus G is tran-sitive on vertices and the stablizer G_a of a vertex a is transitive on the set г_1(a) 相似文献