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 ...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.展开更多
Let G be a finite group. If |N<sub>G</sub>（R<sub>1</sub>）|=|N<sub>L<sub>n</sub></sub>（q）（R<sub>2</sub>）| for every prime r, where R<sub>1</sub...Let G be a finite group. If |N<sub>G</sub>（R<sub>1</sub>）|=|N<sub>L<sub>n</sub></sub>（q）（R<sub>2</sub>）| for every prime r, where R<sub>1</sub>∈Syl<sub>r</sub> G and R<sub>2</sub>∈Syl<sub>r</sub>（L<sub>n</sub>（q））, then G≌L<sub>n</sub>（q）.展开更多
In this paper, we prove the following theorem： Let p be a prime number, P a Sylow psubgroup of a group G and π = π（G） ／ {p}. If P is seminormal in G, then the following statements hold： 1） G is a p-soluble gro...In this paper, we prove the following theorem： Let p be a prime number, P a Sylow psubgroup of a group G and π = π（G） ／ {p}. If P is seminormal in G, then the following statements hold： 1） G is a p-soluble group and P＇ ≤ Op（G）; 2） lp（G） ≤ 2 and lπ（G） ≤ 2; 3） if a π-Hall subgroup of G is q-supersoluble for some q ∈ π, then G is q-supersoluble.展开更多
In this paper we have completely determined:(1)all almost simple groups which act 2-transitively on one of their sets of Sylow p-subgroups.(2)all non-abelian simple groups T whose automorphism group acts 2-transitivel...In this paper we have completely determined:(1)all almost simple groups which act 2-transitively on one of their sets of Sylow p-subgroups.(2)all non-abelian simple groups T whose automorphism group acts 2-transitively on one of the sets of Sylow p-subgroups of T.(3)all finite groups which are 2-transitive on all their sets of Sylow subgroups.展开更多
Let G be a finite group,p be a prime divisor of|G|,and P be a Sylow p-subgroup of G.We prove that P is normal in a solvable group G if|G:kerφ|_(p′)=φ(1)_(p′)for every nonlinear irreducible monomial p-Brauer charac...Let G be a finite group,p be a prime divisor of|G|,and P be a Sylow p-subgroup of G.We prove that P is normal in a solvable group G if|G:kerφ|_(p′)=φ(1)_(p′)for every nonlinear irreducible monomial p-Brauer characterφof G,where kerφis the kernel ofφandφ(1)_(p′)is the p′-part ofφ(1).展开更多
A method which can be used to determine the structures of 2-Sylow subgroups of K2OF for real quadratic fields F is given.By this method,the structures of the 2-Sylow subgroups of K2OF for some real quadratic fields ar...A method which can be used to determine the structures of 2-Sylow subgroups of K2OF for real quadratic fields F is given.By this method,the structures of the 2-Sylow subgroups of K2OF for some real quadratic fields are determined.The method here is suitable for the non-elementary Abelian case as well as the elementary Abelian case.展开更多
基金The NSF (60776810,10871205) of Chinathe NSF (08JCYBJC13900) of Tianjin
文摘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.
文摘Let G be a finite group. If |N<sub>G</sub>（R<sub>1</sub>）|=|N<sub>L<sub>n</sub></sub>（q）（R<sub>2</sub>）| for every prime r, where R<sub>1</sub>∈Syl<sub>r</sub> G and R<sub>2</sub>∈Syl<sub>r</sub>（L<sub>n</sub>（q））, then G≌L<sub>n</sub>（q）.
文摘In this paper, we prove the following theorem： Let p be a prime number, P a Sylow psubgroup of a group G and π = π（G） ／ {p}. If P is seminormal in G, then the following statements hold： 1） G is a p-soluble group and P＇ ≤ Op（G）; 2） lp（G） ≤ 2 and lπ（G） ≤ 2; 3） if a π-Hall subgroup of G is q-supersoluble for some q ∈ π, then G is q-supersoluble.
基金The first author acknowledges the support of OPR Scholarship of Australia The second author is supported by the National Natural Science Foundation of China.Thanks are also due to the Department of Mathematics,the University of Western Australia,where he
文摘In this paper we have completely determined:(1)all almost simple groups which act 2-transitively on one of their sets of Sylow p-subgroups.(2)all non-abelian simple groups T whose automorphism group acts 2-transitively on one of the sets of Sylow p-subgroups of T.(3)all finite groups which are 2-transitive on all their sets of Sylow subgroups.
基金supported by the Cultivation Programme for Young Backbone Teachers in Henan University of Technology,the Fund of Jiangsu Province(Grant Nos.2018k099B,BK20181451)the National Natural Science Foundation of China(Grant Nos.11926330,11926326,11971189,11771356,11871062,12011530061).
文摘Let G be a finite group,p be a prime divisor of|G|,and P be a Sylow p-subgroup of G.We prove that P is normal in a solvable group G if|G:kerφ|_(p′)=φ(1)_(p′)for every nonlinear irreducible monomial p-Brauer characterφof G,where kerφis the kernel ofφandφ(1)_(p′)is the p′-part ofφ(1).
基金Project supported by the National Natural Science Foundation of China.
文摘A method which can be used to determine the structures of 2-Sylow subgroups of K2OF for real quadratic fields F is given.By this method,the structures of the 2-Sylow subgroups of K2OF for some real quadratic fields are determined.The method here is suitable for the non-elementary Abelian case as well as the elementary Abelian case.
