Thompson＇s theorem indicates that a finite group with a nilpotent maximal subgroup of odd order is solvable. As an important application of Thompson＇s theorem, a finite group is solvable if it has an abelian maximal...Thompson＇s theorem indicates that a finite group with a nilpotent maximal subgroup of odd order is solvable. As an important application of Thompson＇s theorem, a finite group is solvable if it has an abelian maximal subgroup. In this paper, we give some sufficient conditions on the number of non-abelian subgroups of a finite group to be solvable.展开更多
Let X be a connected non-normal 4-valent arc-transitive Cayley graph on a dihedral group Dn such that X is bipartite, with the two bipartition sets being the two orbits of the cyclic subgroup within Dn. It is shown th...Let X be a connected non-normal 4-valent arc-transitive Cayley graph on a dihedral group Dn such that X is bipartite, with the two bipartition sets being the two orbits of the cyclic subgroup within Dn. It is shown that X is isomorphic either to the lexicographic product Cn[2K1] with n 〉 4 even, or to one of the five sporadic graphs on 10, 14, 26, 28 and 30 vertices, respectively.展开更多
Let n be a fixed integer, let R be an （n ＋ 1）!-torsion free semiprime ring with the identity element and let F ： R → R be an additive mapping satisfying the relation F（xn＋2） ∑＋n＋i=1xi-1F（x）2xn＋1-i -∑xnF...Let n be a fixed integer, let R be an （n ＋ 1）!-torsion free semiprime ring with the identity element and let F ： R → R be an additive mapping satisfying the relation F（xn＋2） ∑＋n＋i=1xi-1F（x）2xn＋1-i -∑xnF（x）xn＋1-i for all x 6 R. In this case, we prove that F is of the form 2F（x） = D（x） ＋ ax ＋ xa for all x ∈ R, where D ： R → R is a derivation and a 6 R is some fixed element.展开更多
A Schur ring over a finite group is said to be decomposable if it is the generalized wreath product of Schur rings over smaller groups. In this paper we establish a sufficient condition for a decomposable Schur ring o...A Schur ring over a finite group is said to be decomposable if it is the generalized wreath product of Schur rings over smaller groups. In this paper we establish a sufficient condition for a decomposable Schur ring over the direct product of elementary abelian groups to be a Ci-Schur ring. By using this condition we offer short proofs for some known results on the CI-property for decomposable Schur rings over an elementary abelian group of rank at most 5.展开更多
A finite group G is called a special local 2-nilpotent group if G is not 2-nilpotent,the Sylow 2-subgroup P of G has a section isomorphic to the quaternion group of order 8,Ω(P∩G')≤Z(P)and NG(P)is 2-nilpotent.I...A finite group G is called a special local 2-nilpotent group if G is not 2-nilpotent,the Sylow 2-subgroup P of G has a section isomorphic to the quaternion group of order 8,Ω(P∩G')≤Z(P)and NG(P)is 2-nilpotent.In this paper,it is shown that SL2(q),q>3,is a special local 2-nilpotent group if and only if q^2≡1(mod 16),and that GL2(q),q>3,is a special local 2-nilpotent group if and only if q is odd.Moreover,the solvability of finite groups is also investigated by giving two generalizations of a result from[A note on p-nilpotence and solvability of finite groups,J.Algebra 321(2009)1555-1560].展开更多
基金国家自然科学基金资助项目(10871032)“Agencija za raziskovalno dejavnost Republike Slovenije”Proj mladi raziskovalci“Agencija za raziskovalno dejavnost Republike Slovenije”Research Program(P1-0285)
基金国家自然科学基金资助项目(10871032)“Agencija za raziskovalno dejavnost Republike Slovenije,”proj.mladi raziskovalci“Agencija za raziskovalno dejavnost Republike Slovenije,”research program P1-0285
基金Supported by National Natural Science Foundation of China （Grant No. 10871032）, China Postdoctoral Science Foundation （Grant No. 20100470136） the second author is supported in part by ＂Agencija za raziskovalno dejavnost Republike Slovenije＂, proj. mladi raziskovalci, ＂Agencija za raziskovalno dejavnost Republike Slovenije＂, Research Program P1-0285
文摘Thompson＇s theorem indicates that a finite group with a nilpotent maximal subgroup of odd order is solvable. As an important application of Thompson＇s theorem, a finite group is solvable if it has an abelian maximal subgroup. In this paper, we give some sufficient conditions on the number of non-abelian subgroups of a finite group to be solvable.
基金Supported by "Agencija za raziskovalno dejavnost Republike Slovenije", Research Program P1-0285Slovenian-Hungarian Intergovernmental ScientificTechnological Cooperation Project (Grant No. SI-2/2007)
文摘Let X be a connected non-normal 4-valent arc-transitive Cayley graph on a dihedral group Dn such that X is bipartite, with the two bipartition sets being the two orbits of the cyclic subgroup within Dn. It is shown that X is isomorphic either to the lexicographic product Cn[2K1] with n 〉 4 even, or to one of the five sporadic graphs on 10, 14, 26, 28 and 30 vertices, respectively.
文摘Let n be a fixed integer, let R be an （n ＋ 1）!-torsion free semiprime ring with the identity element and let F ： R → R be an additive mapping satisfying the relation F（xn＋2） ∑＋n＋i=1xi-1F（x）2xn＋1-i -∑xnF（x）xn＋1-i for all x 6 R. In this case, we prove that F is of the form 2F（x） = D（x） ＋ ax ＋ xa for all x ∈ R, where D ： R → R is a derivation and a 6 R is some fixed element.
文摘A Schur ring over a finite group is said to be decomposable if it is the generalized wreath product of Schur rings over smaller groups. In this paper we establish a sufficient condition for a decomposable Schur ring over the direct product of elementary abelian groups to be a Ci-Schur ring. By using this condition we offer short proofs for some known results on the CI-property for decomposable Schur rings over an elementary abelian group of rank at most 5.
基金Shandong Provincial Natural Science Foundation,China(ZR2017MA022)NSFC(11561021 and 11761079)+3 种基金Slovenian Research Agency(research program P1-0285research projects N1-0038,N1-0062,J1-6720,J1-6743,J1-7051,J1-9110)in part by NSFC(11561021)NSFC(11201403 and 11561021).
文摘A finite group G is called a special local 2-nilpotent group if G is not 2-nilpotent,the Sylow 2-subgroup P of G has a section isomorphic to the quaternion group of order 8,Ω(P∩G')≤Z(P)and NG(P)is 2-nilpotent.In this paper,it is shown that SL2(q),q>3,is a special local 2-nilpotent group if and only if q^2≡1(mod 16),and that GL2(q),q>3,is a special local 2-nilpotent group if and only if q is odd.Moreover,the solvability of finite groups is also investigated by giving two generalizations of a result from[A note on p-nilpotence and solvability of finite groups,J.Algebra 321(2009)1555-1560].
