For any prime p, all finite noncyclic p-groups which contain a self-centralizing cyclic normal subgroup are determined by using cohomological techniques. Some applications are given, including a character theoretic de...For any prime p, all finite noncyclic p-groups which contain a self-centralizing cyclic normal subgroup are determined by using cohomological techniques. Some applications are given, including a character theoretic description for such groups.展开更多
Let F be a locally defined formation consisting of locally solvable groups, G a hyper-（ cyclic or finite） locally solvable group and A a noetherian ZG-module with all irreducible ZG-factors being finite. The followi...Let F be a locally defined formation consisting of locally solvable groups, G a hyper-（ cyclic or finite） locally solvable group and A a noetherian ZG-module with all irreducible ZG-factors being finite. The following conclusion is obtained： if G∈F, f（ ∞ ） include f（p）, f（p） ≠φ for each p∈π, and A has no nonzero F central ZG- images, then any extension E of A by G splits conjugately over A, and A has no nonzero F central ZG-factors.展开更多
Let Fbe a locally defined formation consisting of locally soluble groups, G a hyper-(cyclic or finite) locally soluble group and A a noetherian ZG-module with all irreducible ZG-factors being finite, G∈F, f(∞)f(p), ...Let Fbe a locally defined formation consisting of locally soluble groups, G a hyper-(cyclic or finite) locally soluble group and A a noetherian ZG-module with all irreducible ZG-factors being finite, G∈F, f(∞)f(p), f(p)≠ for each p∈π. The following conclutions are obtained: (1) if there exists a maximal submodule B of A such that A/B is F-central in G and B has no nonzero F-central ZG-factors, then A has an F-decomposition; (2) if there exists an irreducible F-central submodule B of A such that all ZG-composition factors of A/B are F-ecentric, then A has an F-decomposition.展开更多
Let (?) be a formation locally defined by f(P), G ∈ (?) and A a ZG-module, where p ∈ π = { all primes and symbol ∞}. Then a p-main-factor U/V of G is said to be (?)-central in G if G/CG(U/V) ∈f(p). In this paper,...Let (?) be a formation locally defined by f(P), G ∈ (?) and A a ZG-module, where p ∈ π = { all primes and symbol ∞}. Then a p-main-factor U/V of G is said to be (?)-central in G if G/CG(U/V) ∈f(p). In this paper, we have proved that: let (?) be a locally defined formation consisting of locally soluble groups, G a hyper-(cyclic or finite) locally soluble group and A an artinian ZG-module with all irreducible ZG-factors of A being finite; if G ∈ (?), f(∞) ≡ f(p) . f(p)≠φ for each p ∈ π, A has an (?)-decomposition.展开更多
A series of activated carbons（ACs） were prepared using HNO_3,H_2O_2 and steam as activation agents with the aim to introduce functional groups to carbon surface in the ACs preparation process.The effects of concentr...A series of activated carbons（ACs） were prepared using HNO_3,H_2O_2 and steam as activation agents with the aim to introduce functional groups to carbon surface in the ACs preparation process.The effects of concentration of activation agent,activation time on the surface functional groups and redox property of ACs were characterized by Temperature Program Desorption（TPD） and Cyclic Voltammetry（CV）.Results showed that lactone groups of ACs activated by HNO_3 increase with activation time,and the carboxyl groups increase with the concentration of HNO_3.Carbonyl/quinine groups of ACs activated by H_2O_2 increase with the activation time and the concentration of H_2O_2,although the acidic groups decrease with the concentration of H_2O_2.The redox property reflected by CV at 0 and 0.5 V is different with any kinds of oxygen functional groups characterized by TPD,but it is consistent with the SO_2 catalytic oxidization /oxidation properties indicated by TPR.展开更多
基金Supported by the NSF of China(11171194)by the NSF of Shanxi Province(2012011001-1)
文摘For any prime p, all finite noncyclic p-groups which contain a self-centralizing cyclic normal subgroup are determined by using cohomological techniques. Some applications are given, including a character theoretic description for such groups.
文摘Let F be a locally defined formation consisting of locally solvable groups, G a hyper-（ cyclic or finite） locally solvable group and A a noetherian ZG-module with all irreducible ZG-factors being finite. The following conclusion is obtained： if G∈F, f（ ∞ ） include f（p）, f（p） ≠φ for each p∈π, and A has no nonzero F central ZG- images, then any extension E of A by G splits conjugately over A, and A has no nonzero F central ZG-factors.
基金TheNationalNaturalScienceFoundationofChina (No .10 1710 74 )
文摘Let Fbe a locally defined formation consisting of locally soluble groups, G a hyper-(cyclic or finite) locally soluble group and A a noetherian ZG-module with all irreducible ZG-factors being finite, G∈F, f(∞)f(p), f(p)≠ for each p∈π. The following conclutions are obtained: (1) if there exists a maximal submodule B of A such that A/B is F-central in G and B has no nonzero F-central ZG-factors, then A has an F-decomposition; (2) if there exists an irreducible F-central submodule B of A such that all ZG-composition factors of A/B are F-ecentric, then A has an F-decomposition.
文摘Let (?) be a formation locally defined by f(P), G ∈ (?) and A a ZG-module, where p ∈ π = { all primes and symbol ∞}. Then a p-main-factor U/V of G is said to be (?)-central in G if G/CG(U/V) ∈f(p). In this paper, we have proved that: let (?) be a locally defined formation consisting of locally soluble groups, G a hyper-(cyclic or finite) locally soluble group and A an artinian ZG-module with all irreducible ZG-factors of A being finite; if G ∈ (?), f(∞) ≡ f(p) . f(p)≠φ for each p ∈ π, A has an (?)-decomposition.
基金part of the Innovation Program for Undergraduate supported by China University of Mining & Technology,Beijing.
文摘A series of activated carbons（ACs） were prepared using HNO_3,H_2O_2 and steam as activation agents with the aim to introduce functional groups to carbon surface in the ACs preparation process.The effects of concentration of activation agent,activation time on the surface functional groups and redox property of ACs were characterized by Temperature Program Desorption（TPD） and Cyclic Voltammetry（CV）.Results showed that lactone groups of ACs activated by HNO_3 increase with activation time,and the carboxyl groups increase with the concentration of HNO_3.Carbonyl/quinine groups of ACs activated by H_2O_2 increase with the activation time and the concentration of H_2O_2,although the acidic groups decrease with the concentration of H_2O_2.The redox property reflected by CV at 0 and 0.5 V is different with any kinds of oxygen functional groups characterized by TPD,but it is consistent with the SO_2 catalytic oxidization /oxidation properties indicated by TPR.
