Let G be a finite group. A subgroup H of G is called an H-subgroup in G if NG（H）∩ H^g ≤ H for all g C G. A subgroup H of G is called a weakly H-subgroup in G if there exists a normal subgroup K of G such that G = ...Let G be a finite group. A subgroup H of G is called an H-subgroup in G if NG（H）∩ H^g ≤ H for all g C G. A subgroup H of G is called a weakly H-subgroup in G if there exists a normal subgroup K of G such that G = HK and H N K is an H-subgroup in G. In this paper, we investigate the structure of the finite group G under the assumption that every subgroup of G of prime order or of order 4 is a weakly H-subgroup in G. Our results improve and generalize several recent results in the literature.展开更多
Let F be a saturated formation containing the class of supersolvable groups and let G be a finite group. The following theorems are shown： （1） G ∈ F if and only if there is a normal subgroup H such that G/H ∈ F a...Let F be a saturated formation containing the class of supersolvable groups and let G be a finite group. The following theorems are shown： （1） G ∈ F if and only if there is a normal subgroup H such that G/H ∈ F and every maximal subgroup of all Sylow subgroups of H is either c-normal or s-quasinormally embedded in G; （2） G ∈F if and only if there is a soluble normal subgroup H such that G/H∈F and every maximal subgroup of all Sylow subgroups of F（H）, the Fitting subgroup of H, is either e-normally or s-quasinormally embedded in G.展开更多
Let G be a finite group.The question how the properties of its minimal subgroups influence the structure of G is of considerable interest for some scholars.In this paper we try to use c-normal condition on minimal sub...Let G be a finite group.The question how the properties of its minimal subgroups influence the structure of G is of considerable interest for some scholars.In this paper we try to use c-normal condition on minimal subgroups to characterize the structure of G.Some previously known results are generalized.展开更多
An operator T on a separable,infinite dimensional,complex Hilbert space H is called conjugate normal if C|T|C=|T^(*)| for some conjugate linear,isometric involution C on H.This paper focuses on the invariance of conju...An operator T on a separable,infinite dimensional,complex Hilbert space H is called conjugate normal if C|T|C=|T^(*)| for some conjugate linear,isometric involution C on H.This paper focuses on the invariance of conjugate normality under similarity.Given an operator T,we prove that every operator A similar to T is conjugate normal if and only if there exist complex numbersλ_(1),λ_(2)such that(T-λ_(1))(T-λ_(2))=0.展开更多
基金supported by the Deanship of Scientific Research(DSR) at King Abdulaziz University(KAU) represented by the Unit of Research Groups through the grant number(MG/31/01) for the group entitled "Abstract Algebra and its Applications"
文摘Let G be a finite group. A subgroup H of G is called an H-subgroup in G if NG（H）∩ H^g ≤ H for all g C G. A subgroup H of G is called a weakly H-subgroup in G if there exists a normal subgroup K of G such that G = HK and H N K is an H-subgroup in G. In this paper, we investigate the structure of the finite group G under the assumption that every subgroup of G of prime order or of order 4 is a weakly H-subgroup in G. Our results improve and generalize several recent results in the literature.
基金the Natural Science Foundation of Chinathe Natural Science Foundation of Guangxi Autonomous Region (No.0249001)
文摘Let F be a saturated formation containing the class of supersolvable groups and let G be a finite group. The following theorems are shown： （1） G ∈ F if and only if there is a normal subgroup H such that G/H ∈ F and every maximal subgroup of all Sylow subgroups of H is either c-normal or s-quasinormally embedded in G; （2） G ∈F if and only if there is a soluble normal subgroup H such that G/H∈F and every maximal subgroup of all Sylow subgroups of F（H）, the Fitting subgroup of H, is either e-normally or s-quasinormally embedded in G.
基金The author is supported in part by NSF of China and NSF of Guangdong Province
文摘Let G be a finite group.The question how the properties of its minimal subgroups influence the structure of G is of considerable interest for some scholars.In this paper we try to use c-normal condition on minimal subgroups to characterize the structure of G.Some previously known results are generalized.
基金supported by the National Natural Science Foundation of China (Grant No.12171195).
文摘An operator T on a separable,infinite dimensional,complex Hilbert space H is called conjugate normal if C|T|C=|T^(*)| for some conjugate linear,isometric involution C on H.This paper focuses on the invariance of conjugate normality under similarity.Given an operator T,we prove that every operator A similar to T is conjugate normal if and only if there exist complex numbersλ_(1),λ_(2)such that(T-λ_(1))(T-λ_(2))=0.
