4 citations · 9 across the 12 of their papers we have counts for
13 papers
Non-solvable -arc-transitive covers of Petersen graphs
Jiyong Chen, Cai Heng Li, Ci Xuan Wu +1
We construct connected -arc-transitive covers of the Petersen graph with non-solvable transformation groups, solving the long-standing problem for the existence of such covers.
Finite semiprimitive permutation groups of rank
Cai Heng Li, Hanyue Yi, Yan Zhou Zhu
A transitive permutation group is said to be semiprimitive if each of its normal subgroups is either semiregular or transitive.The class of semiprimitive groups properly contains p…
Finite imprimitive rank affine groups -- I
Cai Heng Li, Luyi Liu, Hanyue Yi +1
This is one of a series of papers which aims towards a classification of imprimitive affine groups of rank . In this paper, a complete classification is given of such groups of…
Coverings of Groups, Regular Dessins, and Surfaces
Jiyong Chen, Wenwen Fan, Cai Heng Li +1
A coset geometry representation of regular dessins is established, and employed to describe quotients and coverings of regular dessins and surfaces. A characterization is then give…
The exceptional Hall numbers
Zheng Guo, Yong Hu, Cai Heng Li
A positive integer is called a Hall number if any finite group of order precisely divisible by has a Hall subgroup of order . We prove that, except for the obvious examp…
Fixers and derangements of finite permutation groups
Hong Yi Huang, Cai Heng Li, Yi Lin Xie
Let be a finite transitive permutation group with point stabiliser . We say that a subgroup of is a fixer if every element of has fixed p…
Locally primitive block designs
Jianfu Chen, Peice Hua, Cai Heng Li +1
A locally primitive 2-design is a 2-design admitting an automorphism group with primitive local actions. It is proved that is point-primitive, and either is an almost s…
The finite groups with three automorphism orbits
Cai Heng Li, Yan Zhou Zhu
A complete classification is given of finite groups whose elements are partitioned into three orbits by the automorphism groups, solving the long-standing classification problem in…
A proof of {Gross}' conjecture on -automorphic -groups
Cai Heng Li, Yan Zhou Zhu
Building upon previous results, a classification is given of finite -groups of which subgroups of order are all fused. This completes the classification problem dated back t…
On finite permutation groups of rank three
Hong Yi Huang, Cai Heng Li, Yan Zhou Zhu
The classification of the finite primitive permutation groups of rank was completed in the 1980s and this landmark achievement has found a wide range of applications. In the ge…
Covers and pseudocovers of symmetric graphs
Cai Heng Li, Yan Zhou Zhu
We introduce the concept of pseudocover, which is a counterpart of cover, for symmetric graphs. The only known example of pseudocovers of symmetric graphs so far was given by Praeg…
The Exact Factorizations of Almost Simple Groups
Cai Heng Li, Lei Wang, Binzhou Xia
This paper presents a classification of exact factorizations of almost simple groups, which has been a long-standing open problem initiated around 1980 by the work of Wiegold-Willi…
Arc-transitive digraphs with quasiprimitive local actions
Michael Giudici, S. P. Glasby, Cai Heng Li +1
Let be a finite -vertex-transitive digraph. The in-local action of is the permutation group induced by the vertex-stabiliser on the set of in-neighbours of …