A simple undirected regular graph is said to be semisymmetric if it is edge-transitive but not vertex-transitive.For a semisymmetric graphΓof order 2p^(3),p a prime,it is well known thatΓis bipartite with two bipart...A simple undirected regular graph is said to be semisymmetric if it is edge-transitive but not vertex-transitive.For a semisymmetric graphΓof order 2p^(3),p a prime,it is well known thatΓis bipartite with two biparts having equal size.The complete classification of such graphs has been given for the full automorphism group Aut(Γ)acting unfaithfully on at least one bipart ofΓ,which shows that there is only one infinite family of such graphs with valency p^(2).The graphs of this kind have been determined when Aut(Γ)acts faithfully and primitively on at least one bipart ofΓ,and thus there is only one remaining case for classifying such graphs of valency p^(2),Aut(Γ)acting faithfully and imprimitively on both biparts ofΓ,which is dealt with in this paper.As a result,there is only one infinite family of semisymmetric graphs of order 2p^(3)with valency p^(2).展开更多
In this paper we investigate the amalgams (M11,X) of rank 2 and characteristic 3,where X is a group of Lie type of rank 1 or permutation group of low rank,and give a characterization of the 3 local subgroups of the fi...In this paper we investigate the amalgams (M11,X) of rank 2 and characteristic 3,where X is a group of Lie type of rank 1 or permutation group of low rank,and give a characterization of the 3 local subgroups of the finite sporadic groups Co3 of Ly and Suz.展开更多
A graph Γ is said to be symmetric if its automorphism group Aut(Γ)acts transitively on the arc set of Γ.We show that if Γ is a finite connected heptavalent symmetric graph with solvable stabilizer admitting a vert...A graph Γ is said to be symmetric if its automorphism group Aut(Γ)acts transitively on the arc set of Γ.We show that if Γ is a finite connected heptavalent symmetric graph with solvable stabilizer admitting a vertex-transitive non-abelian simple group G of automorphisms,then either G is normal in Aut(Γ),or Aut(Γ)contains a non-abelian simple normal subgroup T such that G≤T and(G,T)is explicitly given as one of 11 possible exceptional pairs of non-abelian simple groups.If G is arc-transitive,then G is always normal in Aut(Γ),and if G is regular on the vertices of Γ,then the number of possible exceptional pairs(G,T)is reduced to 5.展开更多
In this paper,we present a complete list of connected arc-transitive graphs of square-free order with valency 11.The list includes the complete bipartite graph K11,11,the normal Cayley graphs of dihedral groups and th...In this paper,we present a complete list of connected arc-transitive graphs of square-free order with valency 11.The list includes the complete bipartite graph K11,11,the normal Cayley graphs of dihedral groups and the graphs associated with the simple group J1 and PSL(2,p),where p is a prime.展开更多
设 G 为有限群,那么 G 的 FF—模的研究在研究包含 G 的抛物系(G,P_1,P_2,B)中起很重要的作用,而 G 的 FF—模的研究又主要归结于抛物系中关于有限群阶的不等式的证明.本文先证明了抛物系中有限群的阶不等式的一个结果,并由此得到了关...设 G 为有限群,那么 G 的 FF—模的研究在研究包含 G 的抛物系(G,P_1,P_2,B)中起很重要的作用,而 G 的 FF—模的研究又主要归结于抛物系中关于有限群阶的不等式的证明.本文先证明了抛物系中有限群的阶不等式的一个结果,并由此得到了关于弱李型单群结果的一个简化证明.展开更多
基金partially supported by the Mathematical Tianyuan Foundation of China(11426093,12126317)National Natural Science Foundation of China(11501172,11301154)+1 种基金Natural Science Foundation of Henan Province,Fundamental Research Funds for the Universities of Henan Province(NSFRF240316)Young Core Teacher Foundation of Henan Polytechnic University(2023XQG-11).
文摘A simple undirected regular graph is said to be semisymmetric if it is edge-transitive but not vertex-transitive.For a semisymmetric graphΓof order 2p^(3),p a prime,it is well known thatΓis bipartite with two biparts having equal size.The complete classification of such graphs has been given for the full automorphism group Aut(Γ)acting unfaithfully on at least one bipart ofΓ,which shows that there is only one infinite family of such graphs with valency p^(2).The graphs of this kind have been determined when Aut(Γ)acts faithfully and primitively on at least one bipart ofΓ,and thus there is only one remaining case for classifying such graphs of valency p^(2),Aut(Γ)acting faithfully and imprimitively on both biparts ofΓ,which is dealt with in this paper.As a result,there is only one infinite family of semisymmetric graphs of order 2p^(3)with valency p^(2).
基金Project supported by the National Natural Science Foundation of China
文摘In this paper we investigate the amalgams (M11,X) of rank 2 and characteristic 3,where X is a group of Lie type of rank 1 or permutation group of low rank,and give a characterization of the 3 local subgroups of the finite sporadic groups Co3 of Ly and Suz.
基金supported by the National Natural Science Foundation of China(11571035,11731002)the 111 Project of China(B16002).
文摘A graph Γ is said to be symmetric if its automorphism group Aut(Γ)acts transitively on the arc set of Γ.We show that if Γ is a finite connected heptavalent symmetric graph with solvable stabilizer admitting a vertex-transitive non-abelian simple group G of automorphisms,then either G is normal in Aut(Γ),or Aut(Γ)contains a non-abelian simple normal subgroup T such that G≤T and(G,T)is explicitly given as one of 11 possible exceptional pairs of non-abelian simple groups.If G is arc-transitive,then G is always normal in Aut(Γ),and if G is regular on the vertices of Γ,then the number of possible exceptional pairs(G,T)is reduced to 5.
基金supported by the National Natural Science Foundation of China(11731002,11701503,11971248,12061089)and the Fundamental Research Funds for the Central Universities.
文摘In this paper,we present a complete list of connected arc-transitive graphs of square-free order with valency 11.The list includes the complete bipartite graph K11,11,the normal Cayley graphs of dihedral groups and the graphs associated with the simple group J1 and PSL(2,p),where p is a prime.
