Let A be a completely decomposable homogeneous torsion-free abelian group of rank n(n≥2).Let m(n)=A×(a)be the split extension of A by an automorphismαwhich is a cyclic permutation of the direct components twist...Let A be a completely decomposable homogeneous torsion-free abelian group of rank n(n≥2).Let m(n)=A×(a)be the split extension of A by an automorphismαwhich is a cyclic permutation of the direct components twisted by a rational integer m.Then Om(n)is an infinite soluble group.In this paper,the residual finiteness of Om(n)is investigated.展开更多
The principal aim of this paper is to study the regular and transitive subgroup functors in the universe of all finite soluble groups.We prove that they form a complemented and non-modular lattice containing two relev...The principal aim of this paper is to study the regular and transitive subgroup functors in the universe of all finite soluble groups.We prove that they form a complemented and non-modular lattice containing two relevant sublattices.This is the answer to a question(Question 1.2.12)proposed by Skiba(1997)in the finite soluble universe.展开更多
We characterize non-finitely generated soluble groups with the maximalcondition on non-Baer subgroups and prove that a non-Baer soluble group is a Cernikov group or ithas an infinite properly descending series of non-...We characterize non-finitely generated soluble groups with the maximalcondition on non-Baer subgroups and prove that a non-Baer soluble group is a Cernikov group or ithas an infinite properly descending series of non-Baer subgroups.展开更多
Water soluble disperse dyes of either monoazo or anthraquinone types containing the carboxymethylsulfonylgroup（-SO2CH2COOH）were synthesized.Ammonium salts of this type of dyes are more soluble thanother salts.These ...Water soluble disperse dyes of either monoazo or anthraquinone types containing the carboxymethylsulfonylgroup（-SO2CH2COOH）were synthesized.Ammonium salts of this type of dyes are more soluble thanother salts.These dyes are suitable for pad dyeing or printing on polyester fiber and polyester/cottonblends in either weak acid,neutral or weak alkali medium without a dispersing agent.The formation of-SO2CH3 group from -SO2CH2COOH group after fixing on the fiber was proved.展开更多
It is shown that the generalized Baumslag-Solitar graphs which have soluble fundamental groups can be constructed from four simple types of graph by a process of decoration. The method of proof is elementary and emplo...It is shown that the generalized Baumslag-Solitar graphs which have soluble fundamental groups can be constructed from four simple types of graph by a process of decoration. The method of proof is elementary and employs the operations of pinching and contracting edges of graphs.展开更多
In recent years,a series of papers about cover-avoiding property of subgroups appeared and all the studies were connected with chief factors of a finite group.However,about the cover-avoiding property of subgroups for...In recent years,a series of papers about cover-avoiding property of subgroups appeared and all the studies were connected with chief factors of a finite group.However,about the cover-avoiding property of subgroups for non-chief factor,there is no study up to now.The purpose of this paper is to build the theory.Let A be a subgroup of a finite group G and Σ:G0≤G1≤…≤Gn some subgroup series of G.Suppose that for each pair(K,H) such that K is a maximal subgroup of H and G i 1 K < H G i for some i,either A ∩ H = A ∩ K or AH = AK.Then we say that A is Σ-embedded in G.In this paper,we study the finite groups with given systems of Σ-embedded subgroups.The basic properties of Σ-embedded subgroups are established and some new characterizations of some classes of finite groups are given and some known results are generalized.展开更多
Let G be a finite group.Let D={(g,g)|g∈C},the main diagonalsubgroup of G x G.In this paper,we consider the suitable generalized normalities orindex of D in G x G,some interesting results are obtained.
In this paper, we investigate the structure of the groups whose nontrivial normal subgroups have order two. Some properties of this kind of groups are obtained.
We consider groups G such that NG（H）/HCG（H） is cyclic for all H ≤ G. More specifically, we characterise locally nilpotent and supersoluble groups with this property.
The group solubility parameter （GSP） model was used to analyze the liquid-liquid equilibrium （LLE） of ternary and quaternary systems. The GSP parameters are divided into four dimensions representing the four major...The group solubility parameter （GSP） model was used to analyze the liquid-liquid equilibrium （LLE） of ternary and quaternary systems. The GSP parameters are divided into four dimensions representing the four major intermolecular forces. The values of the parameters were determined by regression using the nonlinear SIMPLEX optimization method to fit the LLE data of 548 ternary and 26 quaternary systems selected from the literature. LLE predictions of 8 ternary systems were then made using the fit parameters. Comparison of the results with predictions using the modified UNIFAC model shows that the GSP model has less adjustable parameters to achieve a similar accuracy and that the parameter values are easily acquired by analysis of available data.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11771129,11971155,12071117).
文摘Let A be a completely decomposable homogeneous torsion-free abelian group of rank n(n≥2).Let m(n)=A×(a)be the split extension of A by an automorphismαwhich is a cyclic permutation of the direct components twisted by a rational integer m.Then Om(n)is an infinite soluble group.In this paper,the residual finiteness of Om(n)is investigated.
基金the Ministerio de Economia y Competitividad of Spain (Grant No. MTM2014-54707-C3-1-P)National Natural Science Foundation of China (Grant No. 11271085)the Ministerio de Educacion of Spanish Government (Grant No. AP2010-2764).
文摘The principal aim of this paper is to study the regular and transitive subgroup functors in the universe of all finite soluble groups.We prove that they form a complemented and non-modular lattice containing two relevant sublattices.This is the answer to a question(Question 1.2.12)proposed by Skiba(1997)in the finite soluble universe.
文摘We characterize non-finitely generated soluble groups with the maximalcondition on non-Baer subgroups and prove that a non-Baer soluble group is a Cernikov group or ithas an infinite properly descending series of non-Baer subgroups.
文摘Water soluble disperse dyes of either monoazo or anthraquinone types containing the carboxymethylsulfonylgroup（-SO2CH2COOH）were synthesized.Ammonium salts of this type of dyes are more soluble thanother salts.These dyes are suitable for pad dyeing or printing on polyester fiber and polyester/cottonblends in either weak acid,neutral or weak alkali medium without a dispersing agent.The formation of-SO2CH3 group from -SO2CH2COOH group after fixing on the fiber was proved.
文摘It is shown that the generalized Baumslag-Solitar graphs which have soluble fundamental groups can be constructed from four simple types of graph by a process of decoration. The method of proof is elementary and employs the operations of pinching and contracting edges of graphs.
基金supported by National Natural Science Foundation of China (Grant No.11071229)Chinese Academy of Sciences Visiting Professorship for Senior International Scientists (Grant No.2010T2J12)
文摘In recent years,a series of papers about cover-avoiding property of subgroups appeared and all the studies were connected with chief factors of a finite group.However,about the cover-avoiding property of subgroups for non-chief factor,there is no study up to now.The purpose of this paper is to build the theory.Let A be a subgroup of a finite group G and Σ:G0≤G1≤…≤Gn some subgroup series of G.Suppose that for each pair(K,H) such that K is a maximal subgroup of H and G i 1 K < H G i for some i,either A ∩ H = A ∩ K or AH = AK.Then we say that A is Σ-embedded in G.In this paper,we study the finite groups with given systems of Σ-embedded subgroups.The basic properties of Σ-embedded subgroups are established and some new characterizations of some classes of finite groups are given and some known results are generalized.
基金the NSF of China(Nos.11201082,11471054,11671063),the NSF of Jiangsu Province(No.BK20161265)Cultivation Program for Outstanding Young College Teachersof Guangdong Province(Yq2013061).
文摘Let G be a finite group.Let D={(g,g)|g∈C},the main diagonalsubgroup of G x G.In this paper,we consider the suitable generalized normalities orindex of D in G x G,some interesting results are obtained.
基金Project supported in part by the National Natural Science Foundation of China (Grant No.10871210)Foundation of Guangdong University of Technology (Grant No.093057)
文摘In this paper, we investigate the structure of the groups whose nontrivial normal subgroups have order two. Some properties of this kind of groups are obtained.
文摘We consider groups G such that NG（H）/HCG（H） is cyclic for all H ≤ G. More specifically, we characterise locally nilpotent and supersoluble groups with this property.
文摘The group solubility parameter （GSP） model was used to analyze the liquid-liquid equilibrium （LLE） of ternary and quaternary systems. The GSP parameters are divided into four dimensions representing the four major intermolecular forces. The values of the parameters were determined by regression using the nonlinear SIMPLEX optimization method to fit the LLE data of 548 ternary and 26 quaternary systems selected from the literature. LLE predictions of 8 ternary systems were then made using the fit parameters. Comparison of the results with predictions using the modified UNIFAC model shows that the GSP model has less adjustable parameters to achieve a similar accuracy and that the parameter values are easily acquired by analysis of available data.
