The present paper deals with a subgroup X of a group G is almost normal if the index |G: NG(X)| is finite, while X is nearly normal if it has finite index in the normal closure XG. This paper investigates the structur...The present paper deals with a subgroup X of a group G is almost normal if the index |G: NG(X)| is finite, while X is nearly normal if it has finite index in the normal closure XG. This paper investigates the structure of groups in which every (infinite) subgroup is either almost normal or nearly normal.展开更多
Suppose that A is a subgroup of a group G.A is called to be m-embeddedin G if G has a subnormal subgroup T and a{1<G}-embedded subgroup C such thatG=AT and AnT<C≤A.In this paper,we shall investigate the structu...Suppose that A is a subgroup of a group G.A is called to be m-embeddedin G if G has a subnormal subgroup T and a{1<G}-embedded subgroup C such thatG=AT and AnT<C≤A.In this paper,we shall investigate the structure of finitegroups by using m-embedded subgroups and obtain some new characterization aboutp-supersolvability and generalized hypercentre of finite groups.Some results in Guoand Shum(Arch Math 80:561-569,2003),Ramadan et al.(Arch Math 85:203-210,2005),Tang and Miao(Turk J Math 39:501-506,2015),and Xu and Zhang(Can MathBull 57(4):884-889,2014)are generalized.展开更多
Let G be a finite group,σ={σi|i∈ I}be some partition of the set of all primes and σ(G)={(σi|σi∩ π(G)≠0}.We say that a subgroup H of G is nearly cr-cmbcdded in G if there exists a cr-permutable subgroup T of G...Let G be a finite group,σ={σi|i∈ I}be some partition of the set of all primes and σ(G)={(σi|σi∩ π(G)≠0}.We say that a subgroup H of G is nearly cr-cmbcdded in G if there exists a cr-permutable subgroup T of G such that H∩T is a<r-permutable subgroup of G and H C\T<HaeG^where Haec is the subgroup of H generated by all those subgroups of H which are cr-permutably embedded in G.In this paper,we study the structure of G under the condition that some given subgroups of G are nearly cr-embedded in G.Some known results are generalized.展开更多
文摘The present paper deals with a subgroup X of a group G is almost normal if the index |G: NG(X)| is finite, while X is nearly normal if it has finite index in the normal closure XG. This paper investigates the structure of groups in which every (infinite) subgroup is either almost normal or nearly normal.
基金NSFC(Grant#11271016)and NSFC(Grant#11471055)and Qing Lan project of Jiangsu Province and High-level personnel of support program of Yangzhou University and 333 high-level personnel training project in Jiangsu Province.
文摘Suppose that A is a subgroup of a group G.A is called to be m-embeddedin G if G has a subnormal subgroup T and a{1<G}-embedded subgroup C such thatG=AT and AnT<C≤A.In this paper,we shall investigate the structure of finitegroups by using m-embedded subgroups and obtain some new characterization aboutp-supersolvability and generalized hypercentre of finite groups.Some results in Guoand Shum(Arch Math 80:561-569,2003),Ramadan et al.(Arch Math 85:203-210,2005),Tang and Miao(Turk J Math 39:501-506,2015),and Xu and Zhang(Can MathBull 57(4):884-889,2014)are generalized.
文摘Let G be a finite group,σ={σi|i∈ I}be some partition of the set of all primes and σ(G)={(σi|σi∩ π(G)≠0}.We say that a subgroup H of G is nearly cr-cmbcdded in G if there exists a cr-permutable subgroup T of G such that H∩T is a<r-permutable subgroup of G and H C\T<HaeG^where Haec is the subgroup of H generated by all those subgroups of H which are cr-permutably embedded in G.In this paper,we study the structure of G under the condition that some given subgroups of G are nearly cr-embedded in G.Some known results are generalized.
