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群G的一个Cayley图X=Cay(G,S)称为正规的,如果右乘变换群R(G)在AutX中正规.研究了4m阶拟二面体群G=a,b|a~(2m)=b~2=1,a~b=a~(m+1)的4度Cayley图的正规性,其中m=2~r,且r2,并得到拟二面体群的Cayley图的同构类型. 相似文献
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半二面体群的小度数Cayley图 总被引:1,自引:0,他引:1
群G的一个Cayley图X=Cay(G,S)称为正规的,如果右乘变换群R(G)在Aut X中正规.研究了4m阶半二面体群G=〈a,b a2m=b2=1,ab=am-1〉的3度和4度Cayley图的正规性,其中m=2r且r>2,并得到了几类非正规的Cayley图. 相似文献
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We determine all connected normal edge-transitive Cayley graphs on non-abelian groups with order 4p,where p is a prime number.As a consequence we prove if |G|=2δp,δ=0,1,2 and p prime,then Γ=Cay(G,S) is a connected normal 1/2 arc-transitive Cayley graph only if G=F4p,where S is an inverse closed generating subset of G which does not contain the identity element of G and F 4p is a group with presentation F4p = a,b|ap=b4=1,b-1ab=aλ,where λ2≡-1(mod p). 相似文献
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设(a,b,c)为本原的商高数组,满足a~2+b~2=c~2且2|b.1956年,Jesmanowicz猜想:对任给的正整数n,丢番图方程(na)~x+(nb)~y=(nc)~z仅有正整数解x=y=z=2.令P(n)表示n的所有不同素因子乘积.对商高数组(a,b,c)=(p~(2r)-4,4p~r,p~(2r)+4),其中p为大于3的素数且p■1(mod 8),本文证明在条件P(a)|n或者P(n)a下,Jesmanowicz猜想成立. 相似文献
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管训贵 《数学的实践与认识》2019,(18)
设p为素数,p=4A~2+1+2|A,A∈N~*.运用二次和四次丢番图方程的结果证明了方程G:X~2+4Y~4=pZ~4,gcd(X,Y,Z)=1,除开正整数解(X,Y,Z)=(1,A,1)外,当A≡1(mod4)时,至多还有正整数解(X,Y,Z)满足X=|p(a~2-b~2)~2-4(A(a~2-b~2)±ab)~2|,Y~2=A(a~2-b~2)~2±2ab(a~2-b~2)-4a~2b~2A,Z=a~2+b~2;当A≡3(mod4)时,至多还有正整数解(X,Y,Z)满足X=|4a~2b~2A-(4abA±(a~2-b~2))~2|,Y~2=4a~2b~2A±2ab(a~2-b~2)-A(a~2-b~2)~2,Z=a~2+b~2.这里a,b∈N~*并且ab,gcd(a,b)=1,2|(a+b).同时具体给出了p=5时方程G的全部正整数解. 相似文献
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《数学季刊》2018,(4)
Let p be a prime number and f_2(G) be the number of factorizations G = AB of the group G, where A, B are subgroups of G. Let G be a class of finite p-groups as follows,G = a, b | a~(p~n)= b~(p~m)= 1, a~b= a~(p~(n-1)+1), where n m ≥ 1. In this article, the factorization number f_2(G) of G is computed, improving the results of Saeedi and Farrokhi in [5]. 相似文献
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二面体群D_(2n)的4度正规Cayley图 总被引:4,自引:0,他引:4
设G是有限群,S是G的不包含单位元1的非空子集.定义群G关于S的 Cayley(有向)图X=Cay(G,S)如下:V(x)=G,E(X)={(g,sg)|g∈G,s∈S}. Cayley图X=Cay(G,S)称为正规的如果R(G)在它的全自同构群中正规.图X称为1-正则的如果它的全自同构群在它的弧集上正则作用.本文对二面体群D2n以Z22 为点稳定子的4度正规Cayley图进行了分类. 相似文献
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广义四元数群的4-度Cayley图 总被引:1,自引:0,他引:1
一个有限群称为广义四元数群,若Q4n=〈a,b a2n=1,b2=an,ab=a-1,〉n 3.本文根据广义四元数群Q4p(p为奇素数)中只有两类二元生成子集,且它们在Aut(Q4p)的作用下是传递的.结合具体图形,利用查圈的方法重点地证明了广义四元数群关于这两类二元生成子集的4-度C ay ley图的正规性与正则性,解决了4-度C ay ley图的完全分类问题. 相似文献
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1. IntroductionLet G be a finite group and S a subset of G such that S--1 ~ S, and 1 f S. The Cayleygraph Cay (G, S) is defined as the simple graph with V ~ G, and E = {glgZ I g,'g, or g,'g,6 S, gi, gi E G}. Cay (G, S) is vertex-transitive, and it is connected if and only if (S) = G,i.e. S is a generating set of G[1]. If G = Zn, then Cay (Zn, S) is called a circulant graph. Ithas been proved that any connected Cayley graph on a finite abelian group is hamiltonianl2].Furthermore, … 相似文献
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Let p be an odd prime, and D2p =<a, b|ap = b2 = 1, bab = a-1 the dihedral group of order 2p. In this paper, we completely classify the cubic Cayley graphs on D2p up to isomorphism by means of spectral method. By the way, we show that two cubic Cayley graphs on D2p are isomorphic if and only if they are cospectral. Moreover, we obtain the number of isomorphic classes of cubic Cayley graphs on D2p by using Gauss' celebrated law of quadratic reciprocity. 相似文献
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We prove that any circulant graph of order n with connection set S such that n and the order of ?(S), the subgroup of ? that fixes S set‐wise, are relatively prime, is also a Cayley graph on some noncyclic group, and shows that the converse does not hold in general. In the special case of normal circulants whose order is not divisible by 4, we classify all such graphs that are also Cayley graphs of a noncyclic group, and show that the noncyclic group must be metacyclic, generated by two cyclic groups whose orders are relatively prime. We construct an infinite family of normal circulants whose order is divisible by 4 that are also normal Cayley graphs on dihedral and noncyclic abelian groups. © 2005 Wiley Periodicals, Inc. J Graph Theory 相似文献
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决定了4p(p是奇素数)阶二面体群的连通3度Cayley图的完全分类,并证明4p阶二面体群不是弱3-CI群,从而否定了C.H.Li关于"所有有限群都是弱3-CI群"的猜想 相似文献