Let π be a set of primes and G a π-separable group. Isaacs defines the Bπ characters, which can be viewed as the "π-modular" characters in G, such that the Bp′ characters form a set of canonical lifts f...Let π be a set of primes and G a π-separable group. Isaacs defines the Bπ characters, which can be viewed as the "π-modular" characters in G, such that the Bp′ characters form a set of canonical lifts for the p-modular characters. By using Isaacs' work, Slattery has developed some Brauer's ideals of p-blocks to the π-blocks of a finite π-separable group, generalizing Brauer's three main theorems to the π-blocks. In this paper, depending on Isaacs' and Slattery's work, we will extend the first main theorem for π-blocks.展开更多
Carbon materials were used as supports for Ag catalysts that are prepared using the conventional wet impregnation method, and their catalytic properties for CO selective oxidation in excess hydrogen at temperatures be...Carbon materials were used as supports for Ag catalysts that are prepared using the conventional wet impregnation method, and their catalytic properties for CO selective oxidation in excess hydrogen at temperatures below 483 K were tested. A variety of techniques, e.g. N2 adsorption, XPS, TPD, UV-Vis DRS, TEM and SEM, were used to determine the influence of physical and chemical properties of the carbon on the properties of Ag catalyst. It was found that defects on the carbon surface served as nucleation sites for silver ions, while functional groups on carbon surface induced their reduction to the metallic form. The formation of silver particles on carbon was governed by homogeneous and/or heterogeneous nucleation during the impregnation and subsequent activation processes. The best catalytic performance was obtained with a Ag/carbon black catalyst with a uniform size distribution of silver nanoparticles （about 12 nm）, moderate BET surface area （with a mesoporous structure）, and a limited amount of carbon-oxygen groups. The research indicates that carbon materials are potentially good supports for silver catalysts for preferential oxidation of CO in excess hydrogen.展开更多
Alperin and Broug have given the p-subpairs in a finite group, and proved that there is a Sylow theorem for p-subpairs. For a π-separable group with π-Hall subgroup nilpotent, we prove that there is a π-Sylow theor...Alperin and Broug have given the p-subpairs in a finite group, and proved that there is a Sylow theorem for p-subpairs. For a π-separable group with π-Hall subgroup nilpotent, we prove that there is a π-Sylow theorem for π-subpairs. Note that our π-subpairs are different from what Robinson and Staszewski gave.展开更多
If B is a p-block of a finite group G with a minimal nonabelian defect group D (p is an odd prime number) and (D, b D ) is a Sylow B-subpair of G, then N G (D, b D ) controls B-fusion of G in most cases. This result i...If B is a p-block of a finite group G with a minimal nonabelian defect group D (p is an odd prime number) and (D, b D ) is a Sylow B-subpair of G, then N G (D, b D ) controls B-fusion of G in most cases. This result is of great importance, because we can use it to obtain a complete set of representatives of G-conjugate classes of B-subsections and to calculate the number of ordinary irreducible characters in B. This result is key to the calculation of the structure invariants of the block with a minimal nonablian defect group. On the other hand, we improve Brauer's famous formula k(B) =Σ (ω,b ω ) l(b ω ),where (ω, b ω ) ∈ [(G : sp(B))]. Let p be any prime number, B be a p-block of a finite group G and (D, b D ) be a Sylow B-subpair of G. H is a subgroup of N G (D, b D ) satisfying N G (R, b R ) = N H (R, b R )C G (R), (R, b R ) ∈ A 0 (D, b D ), N G ( w , b w' ) = N H ( w , b w' )C G (w' ), (w' , b w' ) ∈ (D, b D ). If w 1 , . . . , w l is a complete set of representatives of H-conjugate classes of D, then (w 1 , b w 1 ), . . . , (w l , b w l ) is a complete set of representatives of G-conjugate classes of B-subsections in G. In particular, we have k(B) =Σ l j=1 l(b w j ).展开更多
We use the method of local representation and original method of Brauer to study the block with K(B) - L(B) = 1, and get some properties on the defect group and the structure of this kind of blocks. Then,we show that ...We use the method of local representation and original method of Brauer to study the block with K(B) - L(B) = 1, and get some properties on the defect group and the structure of this kind of blocks. Then,we show that K(B) conjecture holds for this kind of blocks.展开更多
In this paper, we obtain two results on Brauers k(B) problem about finite groups under some conditions. Furthermore, we obtain that Olssons conjecture holds under the same conditions on the finite groups.
In this paper, we focus on the structure of p-blocks with defect group satisfying some specialcondition. These special conditions include: two elements of the defect group are conjugate to each other indefect D if and...In this paper, we focus on the structure of p-blocks with defect group satisfying some specialcondition. These special conditions include: two elements of the defect group are conjugate to each other indefect D if and only if they are conjugate to each other in G; the number of conjugacy classes whose p-partis contained in P by conjugacy is not larger than |P|.展开更多
For a p-block B of a finite group G, we give a bound of the order of its defect group D in terms of k(B), the number of the irreducible ordinary characters in B.
This paper aims to introduce some new ideas into the study of submodules in Hilbert spaces of analytic functions. The effort is laid out in the Hardy space over the bidisk H^2(D^2). A closed subspace M in H^2(D^2) is ...This paper aims to introduce some new ideas into the study of submodules in Hilbert spaces of analytic functions. The effort is laid out in the Hardy space over the bidisk H^2(D^2). A closed subspace M in H^2(D^2) is called a submodule if ziM ? M(i = 1, 2). An associated integral operator(defect operator) CM captures much information about M. Using a Kre??n space indefinite metric on the range of CM, this paper gives a representation of M. Then it studies the group(called Lorentz group) of isometric self-maps of M with respect to the indefinite metric, and in finite rank case shows that the Lorentz group is a complete invariant for congruence relation. Furthermore, the Lorentz group contains an interesting abelian subgroup(called little Lorentz group) which turns out to be a finer invariant for M.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.10471085)the BS Foundation of Shandong Province,China(Grant No.03bs006).
文摘Let π be a set of primes and G a π-separable group. Isaacs defines the Bπ characters, which can be viewed as the "π-modular" characters in G, such that the Bp′ characters form a set of canonical lifts for the p-modular characters. By using Isaacs' work, Slattery has developed some Brauer's ideals of p-blocks to the π-blocks of a finite π-separable group, generalizing Brauer's three main theorems to the π-blocks. In this paper, depending on Isaacs' and Slattery's work, we will extend the first main theorem for π-blocks.
基金the Chinese Ministry of Science and Technology (2003CB6 15806) the Natural Science Foundation of China (National Key Project: 90206036).
文摘Carbon materials were used as supports for Ag catalysts that are prepared using the conventional wet impregnation method, and their catalytic properties for CO selective oxidation in excess hydrogen at temperatures below 483 K were tested. A variety of techniques, e.g. N2 adsorption, XPS, TPD, UV-Vis DRS, TEM and SEM, were used to determine the influence of physical and chemical properties of the carbon on the properties of Ag catalyst. It was found that defects on the carbon surface served as nucleation sites for silver ions, while functional groups on carbon surface induced their reduction to the metallic form. The formation of silver particles on carbon was governed by homogeneous and/or heterogeneous nucleation during the impregnation and subsequent activation processes. The best catalytic performance was obtained with a Ag/carbon black catalyst with a uniform size distribution of silver nanoparticles （about 12 nm）, moderate BET surface area （with a mesoporous structure）, and a limited amount of carbon-oxygen groups. The research indicates that carbon materials are potentially good supports for silver catalysts for preferential oxidation of CO in excess hydrogen.
基金Supported by NSF of China(10471085)by BSF of Shandong(03bs006)
文摘Alperin and Broug have given the p-subpairs in a finite group, and proved that there is a Sylow theorem for p-subpairs. For a π-separable group with π-Hall subgroup nilpotent, we prove that there is a π-Sylow theorem for π-subpairs. Note that our π-subpairs are different from what Robinson and Staszewski gave.
文摘If B is a p-block of a finite group G with a minimal nonabelian defect group D (p is an odd prime number) and (D, b D ) is a Sylow B-subpair of G, then N G (D, b D ) controls B-fusion of G in most cases. This result is of great importance, because we can use it to obtain a complete set of representatives of G-conjugate classes of B-subsections and to calculate the number of ordinary irreducible characters in B. This result is key to the calculation of the structure invariants of the block with a minimal nonablian defect group. On the other hand, we improve Brauer's famous formula k(B) =Σ (ω,b ω ) l(b ω ),where (ω, b ω ) ∈ [(G : sp(B))]. Let p be any prime number, B be a p-block of a finite group G and (D, b D ) be a Sylow B-subpair of G. H is a subgroup of N G (D, b D ) satisfying N G (R, b R ) = N H (R, b R )C G (R), (R, b R ) ∈ A 0 (D, b D ), N G ( w , b w' ) = N H ( w , b w' )C G (w' ), (w' , b w' ) ∈ (D, b D ). If w 1 , . . . , w l is a complete set of representatives of H-conjugate classes of D, then (w 1 , b w 1 ), . . . , (w l , b w l ) is a complete set of representatives of G-conjugate classes of B-subsections in G. In particular, we have k(B) =Σ l j=1 l(b w j ).
基金supported by the National Natural Seience Foundation of China(Grant Na.19831070)and RFDP.
文摘We use the method of local representation and original method of Brauer to study the block with K(B) - L(B) = 1, and get some properties on the defect group and the structure of this kind of blocks. Then,we show that K(B) conjecture holds for this kind of blocks.
文摘In this paper, we obtain two results on Brauers k(B) problem about finite groups under some conditions. Furthermore, we obtain that Olssons conjecture holds under the same conditions on the finite groups.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 19831070) and BNSF (1992003).
文摘In this paper, we focus on the structure of p-blocks with defect group satisfying some specialcondition. These special conditions include: two elements of the defect group are conjugate to each other indefect D if and only if they are conjugate to each other in G; the number of conjugacy classes whose p-partis contained in P by conjugacy is not larger than |P|.
基金the National Natural Science Foundation of China (Grant No. 10071061) Fujian Province Science Foundation and Mathematical Center of Ministry of Education of China.
文摘For a p-block B of a finite group G, we give a bound of the order of its defect group D in terms of k(B), the number of the irreducible ordinary characters in B.
基金supported by Grant-in-Aid for Young Scientists(B)(Grant No.23740106)
文摘This paper aims to introduce some new ideas into the study of submodules in Hilbert spaces of analytic functions. The effort is laid out in the Hardy space over the bidisk H^2(D^2). A closed subspace M in H^2(D^2) is called a submodule if ziM ? M(i = 1, 2). An associated integral operator(defect operator) CM captures much information about M. Using a Kre??n space indefinite metric on the range of CM, this paper gives a representation of M. Then it studies the group(called Lorentz group) of isometric self-maps of M with respect to the indefinite metric, and in finite rank case shows that the Lorentz group is a complete invariant for congruence relation. Furthermore, the Lorentz group contains an interesting abelian subgroup(called little Lorentz group) which turns out to be a finer invariant for M.
