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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
2.
目的是研究局部传递图的性质和分类.运用置换群和陪集图的理论,获得了关于素数立方阶群局部传递图的完全分类,证明了这些图是一些互不相交的关于素数立方阶群边传递图的并. 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
5.
一类不能作为自同构群的奇阶群 总被引:2,自引:0,他引:2
本文考虑如下问题:怎样的有限群可以作为另一个有限群的全自同构群?我们首先证明,若有限群K有一个正规Sylowp-子群使得|K:Z(K)|p=p2,那么K有2阶自同构.利用这个结果,我们证明了,若奇阶群G具有阶Psm(1≤s≤3),p为|G|的最小素因子,pm,m无立方因子,则G不可能作为全自同构群. 相似文献
6.
无平方因子阶群的自同构群阶的上确界 总被引:2,自引:0,他引:2
群阶为素数方幂(即p- 群)时已得到该群自同构群阶的上确界,而对于其他情形的群,同样的问题要复杂得多. 本文在群阶无平方因子且为偶数时,给出了这类群的自同构群阶的上确界. 相似文献
7.
The Automorphism Group of a Class of Nilpotent Groups with Infinite Cyclic Derived Subgroups 下载免费PDF全文
The automorphism group of a class of nilpotent groups with infinite cyclic derived subgroups is determined. Let G be the direct product of a generalized extraspecial Z-group E and a free abelian group A with rank m, where E ={(1 kα_1 kα_2 ··· kα_nα_(n+1) 0 1 0 ··· 0 α_(n+2)...............000...1 α_(2n+1)000...01|αi∈ Z, i = 1, 2,..., 2 n + 1},where k is a positive integer. Let AutG G be the normal subgroup of Aut G consisting of all elements of Aut G which act trivially on the derived subgroup G of G, and AutG/ζ G,ζ GG be the normal subgroup of Aut G consisting of all central automorphisms of G which also act trivially on the center ζ G of G. Then(i) The extension 1→ Aut_(G') G→ AutG→ Aut(G')→ 1 is split.(ii) Aut_(G') G/Aut_(G/ζ G,ζ G)G≌Sp(2 n, Z) ×(GL(m, Z)■(Z~)m).(iii) Aut_(G/ζ G,ζ GG/Inn G)≌(Z_k)~(2n)⊕(Z)~(2nm). 相似文献
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All graphs are finite simple undirected and of no isolated vertices in this paper. Using the theory of coset graphs and permutation groups, it is completed that a classification of locally transitive graphs admitting a non-Abelian group with cyclic Sylow subgroups. They are either the union of the family of arc-transitive graphs, or the union of the family of bipartite edge-transitive graphs. 相似文献
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Tao Xu & Heguo Liu 《数学研究通讯:英文版》2016,32(2):167-172
Let G be a finitely generated torsion-free nilpotent group and α an automorphism of prime order p of G. If the map φ : G-→ G defined by gφ= [g, α]is surjective, then the nilpotent class of G is at most h(p), where h(p) is a function depending only on p. In particular, if α3= 1, then the nilpotent class of G is at most2. 相似文献
10.
Hauke Klein 《Geometriae Dedicata》1999,77(3):271-277
We consider a four-dimensional compact projective plane
whose collineation group is six-dimensional and solvable with a nilradical N isomorphic to Nil×R, where Nil denotes the three-dimensional, simply connected, non-Abelian, nilpotent Lie group. We assume that fixes a flag p W, acts transitively on
and fixes no point in the set W\p. Under these conditions, we will prove that either contains a three-dimensional group of elations or acts doubly transitively on
. 相似文献