In this article, we first investigate the properties of modular Frobenius groups. Then, we consider the case that G＇ is a minimal normal subgroup of a modular Frobenius group G. We give the complete classification of...In this article, we first investigate the properties of modular Frobenius groups. Then, we consider the case that G＇ is a minimal normal subgroup of a modular Frobenius group G. We give the complete classification of G when G＇ as a modular Frobenius kernel has no more than four conjugacy classes in G.展开更多
A semidirect product G=F⋋H of groups F and H is called a Frobenius group if the following two conditions are satisfied:(F1)H acts freely on F,that is,fh=f for f in F and h in H only if^(h)=1 or f=1.(F2)Every non-ident...A semidirect product G=F⋋H of groups F and H is called a Frobenius group if the following two conditions are satisfied:(F1)H acts freely on F,that is,fh=f for f in F and h in H only if^(h)=1 or f=1.(F2)Every non-identity element h∈H of finite order n induces in F by conjugation in G a splitting automorphism,that is,ff^(h)⋯fh^(n−1)=1 for every f∈F;in other words,the order of f^(h−1)is equal to n.We describe the normal structure of a Frobenius group with periodic subgroup H generated by elements of order 3.展开更多
A finite group G is called a Camina group if G has a proper normal subgroup N such that gN is precisely a conjugacy class of G for any g ∈E G - N. In this paper, the structure of a Camina group G is determined when N...A finite group G is called a Camina group if G has a proper normal subgroup N such that gN is precisely a conjugacy class of G for any g ∈E G - N. In this paper, the structure of a Camina group G is determined when N is a union of 2, 3 or 4 conjugacy classes of G.展开更多
A new class CP_(2) groups of finite groups was characterized by using an inequality of the orders of elements.In this short paper we give a note of CP_(2) groups since CP_(2) groups is a subclass of CP(EPPO)groups.Mor...A new class CP_(2) groups of finite groups was characterized by using an inequality of the orders of elements.In this short paper we give a note of CP_(2) groups since CP_(2) groups is a subclass of CP(EPPO)groups.Moreover,we discuss the struc-ture of finite p groups contained in CP 2 groups.展开更多
The main object of this paper is to investigate the finite groups in which every subgroup is either abelian or normal. We obtain a characterization of the groups for the nonnilpotent case, and we also give some proper...The main object of this paper is to investigate the finite groups in which every subgroup is either abelian or normal. We obtain a characterization of the groups for the nonnilpotent case, and we also give some properties for the nilpotent case.展开更多
A covering p from a Cayley graph Cay（G, X） onto another Cay（H, Y） is called typical Frobenius if G is a Frobenius group with H as a Frobenius complement and the map p ： G →H is a group epimorphism. In this paper...A covering p from a Cayley graph Cay（G, X） onto another Cay（H, Y） is called typical Frobenius if G is a Frobenius group with H as a Frobenius complement and the map p ： G →H is a group epimorphism. In this paper, we emphasize on the typical Frobenius coverings of Cay（H, Y）. We show that any typical Frobenius covering Cay（G, X） of Cay（H, Y） can be derived from an epimorphism /from G to H which is determined by an automorphism f of H. If Cay（G, X1） and Cay（G, X2） are two isomorphic typical Frobenius coverings under a graph isomorphism Ф, some properties satisfied by Фare given.展开更多
Let N be a normal subgroup of a group G. Suppose that the positive integers m 〉 n are two longest non-central G-conjugacy class sizes of N with （m, n） = 1. The purpose of this paper is to determine the structure of...Let N be a normal subgroup of a group G. Suppose that the positive integers m 〉 n are two longest non-central G-conjugacy class sizes of N with （m, n） = 1. The purpose of this paper is to determine the structure of N and give the N-conjugacy class sizes of the elements in N under that assumption that m is square free.展开更多
基金Supported by the National Natural Science Foundation of China (11171243, 11201385)the Technology Project of Department of Education of Fujian Province(JA12336)+1 种基金the Fundamental Research Funds for the Central Universities (2010121003)the Science and the Natural Science Foundation of Fujian Province (2011J01022)
文摘In this article, we first investigate the properties of modular Frobenius groups. Then, we consider the case that G＇ is a minimal normal subgroup of a modular Frobenius group G. We give the complete classification of G when G＇ as a modular Frobenius kernel has no more than four conjugacy classes in G.
基金The work was supported by the Program of Fundamental Research of the SB RAS no.1.1.1(project no.0314-2019-0001).
文摘A semidirect product G=F⋋H of groups F and H is called a Frobenius group if the following two conditions are satisfied:(F1)H acts freely on F,that is,fh=f for f in F and h in H only if^(h)=1 or f=1.(F2)Every non-identity element h∈H of finite order n induces in F by conjugation in G a splitting automorphism,that is,ff^(h)⋯fh^(n−1)=1 for every f∈F;in other words,the order of f^(h−1)is equal to n.We describe the normal structure of a Frobenius group with periodic subgroup H generated by elements of order 3.
基金The NSF (10771132) of Chinathe Science and Technology Foundation (20081022) of Shanxi Province for Collegesthe Team Innovation Research Foundation of Shanxi University of Finance and Economics
文摘A finite group G is called a Camina group if G has a proper normal subgroup N such that gN is precisely a conjugacy class of G for any g ∈E G - N. In this paper, the structure of a Camina group G is determined when N is a union of 2, 3 or 4 conjugacy classes of G.
基金supported by the Natural Science Foundation of China(Nos.11171364,11671063,11471266).
文摘A new class CP_(2) groups of finite groups was characterized by using an inequality of the orders of elements.In this short paper we give a note of CP_(2) groups since CP_(2) groups is a subclass of CP(EPPO)groups.Moreover,we discuss the struc-ture of finite p groups contained in CP 2 groups.
基金Foundation item： the National Natural Science Foundation of China （No. 10571128）i the Natural Science Foundation of Jiangsu Education Committee （No. 05KJB110002）.
文摘The main object of this paper is to investigate the finite groups in which every subgroup is either abelian or normal. We obtain a characterization of the groups for the nonnilpotent case, and we also give some properties for the nilpotent case.
基金Supported by National Natural Science Foundation of China (Grant Nos.10571005 and 10801114)Natural Science Foundation of Shandong Province (Grant No.Y2007A30)Shan Dong Domestic Visiting Project
文摘A covering p from a Cayley graph Cay（G, X） onto another Cay（H, Y） is called typical Frobenius if G is a Frobenius group with H as a Frobenius complement and the map p ： G →H is a group epimorphism. In this paper, we emphasize on the typical Frobenius coverings of Cay（H, Y）. We show that any typical Frobenius covering Cay（G, X） of Cay（H, Y） can be derived from an epimorphism /from G to H which is determined by an automorphism f of H. If Cay（G, X1） and Cay（G, X2） are two isomorphic typical Frobenius coverings under a graph isomorphism Ф, some properties satisfied by Фare given.
基金Supported by National Natural Science Foundation of China(Grant No.11271301)NSFC-He’nan Joint Fund(Grant No.U1204101)
文摘Let N be a normal subgroup of a group G. Suppose that the positive integers m 〉 n are two longest non-central G-conjugacy class sizes of N with （m, n） = 1. The purpose of this paper is to determine the structure of N and give the N-conjugacy class sizes of the elements in N under that assumption that m is square free.
