共查询到18条相似文献,搜索用时 76 毫秒
1.
有循环极大子群的素数幂阶群的作用是边传递的图(Ⅰ) 总被引:1,自引:1,他引:0
Γ是一个有限的、单的、无向的且无孤立点的图, G是Aut(Γ)的一个子群.如果G在Γ的边集合上传递,则称Γ是G-边传递图.我们完全分类了当G为一个有循环的极大子群的素数幂阶群时的G-边传递图.这扩展了Sander的结果.本文仅给出其中的一种情况,即当G同构于群时,所有的G-边传递图.结果为,是G-边传递的当且仅当Γ为下列图之一 相似文献
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假定Γ是一个有限的、单的、无向的且无孤立点的图,G是Aut(Γ)的一个子群.如果G在Γ的边集合上传递,则称Γ是G-边传递图.我们完全分类了当G为一个有循环的极大子群的素数幂阶群时的G-边传递图.结果为:设图Γ含有一个阶为pn(p是素数,n≥2)的自同构群,且G有一个极大子群循环,则Γ是G-边传递的,当且仅当Γ同构于下列图之一1)pmK1,pn-1-m,0≤m≤n-1;2)pmK1,pn-m,0≤m≤n;3)pmKp,pn-m-1,0≤m≤n-2;4)pn-mCpm,pm≥3,m<n;5)2n-2K1,1;6)pn-1-mCpm,pm≥3,m≤n-1;7)2pn-mCpm,pm≥3,m≤n-1;8)2pn-mK1,pm,0≤m≤n;9)pn-mK1,2pm,0≤m≤n;10)pn-mK2,pm,0<m≤n;11)C(2pn-m,1,pm);12)pkC(2pm-k,1,pn-m),0<k<m,0<m≤n;13)(t-s,2m)C(2m 1/(t-s,2m),1,2n-1-m),其中0≤m≤n-1,2n-2(s-1)≡0(mod 2m),t≡1(mod 2),s(≠)t(mod 2m),1≤s≤2m,1≤t≤2n-1;14)∪p i=1 Ci p n-1,其中Ci p n-1=Ca1a1 [1 (i-1)pn-2]a 1 2[1 (i--1)p n-2]…a 1 (pn-1-1)[1 (i-1)p n-2]≌Cp n-1,i=1,2,…,p;15)∪2 i=1 Ci 2n-1,其中Ci 2n-1=Ca1a 1 [1 (i-1)(2n-2-1)]a1 2[1 (i-1)(2n-2-1)]…a1 (2n-1-1)[1 (i-1)(2n-2-1)]≌C2n-1,i=1,2. 相似文献
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在以前的一些工作中,作者已经证明语言(?)={+,0,e)上素数阶群的理论T有量词消去性质并研究了它的判定问题的复杂性.本文在此基础上将利用T的判定问题的复杂性结果给出理论T的量词消去的一个算法,同时给出该算法的复杂性上界. 相似文献
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本文中我们将研究语言,上素数阶群理论T的量词消去及相应的复杂性.我们证明理论T有量词消去性质,并利用该性质给出理论T判定问题的一个复杂性上界. 相似文献
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高有 《数学物理学报(A辑)》2005,25(4):564-568
设K=F_(q^2),其特征为p, q=p^α,K有对合自同构ω:a→a^q. G是一个p 群,其阶为p^β, 群代数R=KG为一局部环. K的2阶自同构ω可延拓为R的一个2阶自同构,记为ω',为方便,对任意a∈R, 记ω‘(a)为~a. R上2n级酉群定义为U_(2n)R={A∈GL_(2n)R|A(0,I^n,I^n,0)~A^t=(0,I^n,I^n,0)} 该文计算了U_(2n)R的阶. 相似文献
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考察元素的阶如何影响有限群的结构是群论中的一个重要课题.本文研究存在一个正规子群N,N外的元素都是素数阶元的有阶群.主要利用熟知的Thompson的一个定理,获得了这样的有限群. 相似文献
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如果图X的全自同构群Aut(X)作用在其顶点集V(X)和边集E(X)上都是传递的,但作用在弧集Arc(X)上非传递,则称X是半传递图.研究了4p~2(p3且p≡-1(mod4))阶4度半传递图,确定了4p~2阶4度半传递图的连通性及其自同构群的阶. 相似文献
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Let F be a finite simple undirected graph with no isolated vertices. Let p, q be prime numbers with p≥q. We complete the classification of the graphs on which a group of order pq acts edge-transitively. The results are the following. If Aut(Г) contains a subgroup G of order pq that acts edge-transitively on F, then F is one of the following graphs: (1) pK1,1; (2) pqK1,1; (3) pgq,1; (4) qKp,1 (p 〉 q); (5) pCq (q 〉 2); (6) qCp (p 〉 q); (7) Cp (p 〉 q = 2); (8) Cpq; (9) (Zp, C) whereC={±r^μ |μ∈Zq} withq〉2, q|(p-1) and r≠1≡r^q (modp); (10) Kp,1 (p 〉 q); (11) a double Cayley graph B(G,C) with C = {1-r^μ | μ ∈ Zq} and r≠1≡r^q (modp); (12) Kpq,1;or (13) Kp,q. 相似文献
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《高校应用数学学报(英文版)》2010,(4)
Let Γ be a finite simple undirected graph with no isolated vertices. Let p, q be prime numbers with p ≥ q. We complete the classification of the graphs on which a group of order pq acts edge-transitively. The results are the following. If Aut(Γ) contains a subgroup G of order pq that acts edge-transitively on Γ, then Γ is one of the following graphs: (1) pK 1,1 ; (2) pqK 1,1 ; (3) pK q,1 ; (4) qK p,1 (p q); (5) pC q (q 2); (6) qC p (p q); (7) C p (p q = 2); (8) C pq ; (9) (Z p , C) where C = {±rμ | μ∈ Z q } with q 2, q|(p-1) and r ≡ 1 ≡ r q (mod p); (10) K p,1 (p q); (11) a double Cayley graph B(G, C) with C = {1-r μ | μ∈ Z q } and r ≡ 1 ≡ r q (mod p); (12) K pq,1 ; or (13) K p,q . 相似文献
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M. R. DARAFSHEH 《数学学报(英文版)》2008,24(7):1117-1126
The author will prove that the group ^2Dp(3) can be uniquely determined by its order components, where p ≠ 2^m + 1 is a prime number, p ≥ 5. More precisely, if OC(G) denotes the set of order components of G, we will prove OC(G) = OC(^2Dp(3)) if and only if G is isomorphic to ^2Dp(3). A main consequence of our result is the validity of Thompson's conjecture for the groups under consideration. 相似文献
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For a finite group G, let πe(G) be the set of order of elements in G and denote S
n the symmetric group on n letters. We will show that if πe(G ) = πe(H), where H is S
p or S
p+1 and p is a prime with 50 < p < 100, then G
≅ H.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
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A graph is called edge-transitive if its full automorphism group acts transitively on its edge set.In this paper,by using classification of finite simple groups,we classify tetravalent edge-transitive graphs of order p2q with p,q distinct odd primes.The result generalizes certain previous results.In particular,it shows that such graphs are normal Cayley graphs with only a few exceptions of small orders. 相似文献
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Bo Qing Xue 《数学学报(英文版)》2014,30(11):1861-1866
Let Fp be the finite field of p elements with p prime.If A is a subset of Fp and g is an element of F*p with order ν,then max{|A + g·A|,|A·A|} (ν/(ν + |A|2) )1/12|A|13/12. 相似文献
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Let G be a finite group. We define the prime graph Γ(G) as follows. The vertices of Γ(G) are the primes dividing the order of G and two distinct vertices p, q are joined by an edge if there is an element in G of order pq. Recently M. Hagie [5] determined finite groups G satisfying Γ(G) = Γ(S), where S is a sporadic simple group. Let p > 3 be a prime number. In this paper we determine finite groups G such that Γ(G) = Γ(PSL(2, p)). As a consequence of our results we prove that if p > 11 is a prime number and p ≢ 1 (mod 12), then PSL(2, p) is uniquely determined by its prime graph and so these groups are characterizable by their prime graph.
The third author was supported in part by a grant from IPM (No. 84200024). 相似文献
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Evrim Akalan 《代数通讯》2017,45(2):694-697
Let R be a commutative Noetherian domain and A be a polycyclic-by-finite group. In this paper, it is determined, in terms of properties of R and A when the group ring R[A] is a G-Dedekind prime ring. 相似文献