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Cubic vertex-transitive non-Cayley graphs of order 12p

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Science China Mathematics 2018年第6期61卷 1153-1162页

作者： Wei-Juan Zhang Yan-Quan Feng Jin-Xin Zhou Department of Mathematics Beijing Jiaotong University Beijing 100044 China

A graph is said to be vertex-transitive non-Cayley if its full automorphism group acts transitively on its vertices and contains no subgroups acting regularly on its vertices. In this paper, a complete classification of cubic vertex-transitive non-Cayley graphs of order 12 p, where p is a prime, is given. As a result, there are 11 sporadic and one infinite family of such graphs, of which the sporadic ones occur when p equals 5, 7 or 17, and the infinite family exists if and only if p ≡ 1(mod 4), and in this family there is a unique graph for a given order.

关键词： Cayley graphs vertex-transitive graphs automorphism groups

On q-n-gonal Klein Surfaces

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Acta Mathematica Sinica,English Series 2007年第10期23卷 1833-1844页

作者： B.ESTRADA R.A.HIDALGO E.MARTINEZ Departamento de Matemáticas Fundamentales UNEDPaseo Senda del Rey 928040 MadridSpain Departamento de Matemática Universidad Técnica Federico Santa MaríaCasilla 110-V ValparaisoChile

We consider proper Klein surfaces X of algebraic genus p ≥ 2, having an automorphism φ of prime order n with quotient space X/（φ） of algebraic genus q. These Klein surfaces axe called q-n-gonal surfaces and they are n-sheeted covers of surfaces of algebraic genus q. In this paper we extend the results of the already studied cases n ≤ 3 to this more general situation. Given p ≥ 2, we obtain, for each prime n, the （admissible） values q for which there exists a q-n-gonal surface of algebraic genus p. Furthermore, for each p and for each admissible q, it is possible to check all topological types of q-n-gonal surfaces with algebraic genus p. Several examples are given： q-pentagonal surfaces and q-n-gonal bordered surfaces with topological genus g = 0, 1.

关键词： Klein surfaces Riemann surfaces automorphism groups non-Euclidean crystallographic groups

On Block-transitive 6-（v, k, λ）-Designs with k at Most 10000

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Algebra Colloquium 2014年第2期21卷 231-234页

作者： Qionghua Tan Weijun Liu Jing Chen School of Mathematics Central South University Changsha Hunan 410075 China School of Mathematics and Physics Nanhua University Hengyang Hunan 421001 China

In recent years, there has been a great deal of research concerning the flag- transitive t-designs, however, few about the block-transitive t-designs with t large （t 〉 4）. In 1993, Cameron and Praeger conjectured that there are no non-trivial block-transitive 6-designs. In this paper, we prove that the conjecture is true when k ≤ 10000 and G ≤ Aut（D） is almost simple.

关键词： block-transitive 6-designs 3-homogeneous automorphism groups

Characterization of convex domains in C^2 with non-compact automorphism group

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Science China Mathematics 2017年第6期60卷 977-984页

作者： HAMANN Kaylee WONG Bun Department of Mathematics University of California at Riverside

In the field of several complex variables, the Greene-Krantz Conjecture, whose consequences would be far reaching, has yet to be proven. The conjecture is as follows： Let D be a smoothly bounded domain in Cn. Suppose there exists {gj} C Aut（D） such that {gj（z）} accumulates at a boundary point p ∈δD for some z C D. Then DD is of finite type at p. In this paper, we prove the following result, yielding further evidence to the probable veracity of this important conjecture： Let D be a bounded convex domain in C2 with C2 boundary. Suppose that there is a sequence {gj} Aut（D） such that {gj（z）} accumulates at a boundary point for some point z ∈ D. Then if p E OD is such an orbit accumulation point, OD contains no non-trivial analytic variety passing through p.

关键词： characterization convex domains automorphism groups

Some new 3-designs from P SL(2,q) with q ≡ 1(mod 4)

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Science China Mathematics 2012年第9期55卷 1901-1911页

作者： LIU WeiJun TANG JianXiong WU YiXiangt School of Science Nantong University Nantong 226007 China Department of Education Science Hunan First Normal University-Changsha '410002 China School of Mathematics and Statistics Central South University Changsha 410075 China

We determine the sizes of orbits from the action of subgroups of PSL(2,q) on projective line X = GF(q) ∪ {∞} with q a prime power and congruent to 1 modulo *** an example of its application,we construct some new fam... 详细信息

关键词： simple 3-designs projective special linear groups projective line automorphism groups

The automorphism Group of U（4,Z）

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Chinese Quarterly Journal of Mathematics 2012年第1期27卷 98-103页

作者： WANG Yu-lei SUN Da-wei WANG Zhi-jun Department of Mathematics Henan University of TechnologyZhengzhou 450001China Department of Mathematics China University of Mining and TechnologyXuzhou 221116China

In this paper,the automorphism group of G is determined,where G is a 4 × 4 upper unitriangular matrix group over *** K be the subgroup of AutG consisting of all elements of AutG which act trivially on G/G,G /ζG and ζG,then (i) InnG ■ K ■ AutG;(ii) AutG/K≌=G_1×D_8×Z_2,where G_1=(a,b,c|a^4=b^2=c^2=1,a^b=a^(-1),[a,c]= [b,c]=1 ;(iii) K/Inn G≌=Z×Z×Z.

关键词： upper unitriangular matrix groups general linear groups automorphism groups