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
Let G be a polycyclic group and α a regular automorphism of order four of G. If the map φ: G→ G defined by g;= [g, α] is surjective, then the second derived group of G is contained in the centre of G. Abandoning t...Let G be a polycyclic group and α a regular automorphism of order four of G. If the map φ: G→ G defined by g;= [g, α] is surjective, then the second derived group of G is contained in the centre of G. Abandoning the condition on surjectivity, we prove that C;（α;） and G/[G, α;] are both abelian-by-finite.展开更多
The structure of groups in which many subgroups have a certain property X has been investigated for several choices of the property χ.In particular, groups whose non-normal subgroups are supersoluble are studied ia t...The structure of groups in which many subgroups have a certain property X has been investigated for several choices of the property χ.In particular, groups whose non-normal subgroups are supersoluble are studied ia this paper. Moreover, groups with only finitely many normalizers of non-supersoluble groups are considered.展开更多
Let G be a group,and let a be a regular automorphism of order p2 of G,where p is a prime.If G is polycyclic-by-finite and the map φ:G→G defined by=g^φ,[g,a]is surjective,then G is soluble.If G is polycyclic,then CG...Let G be a group,and let a be a regular automorphism of order p2 of G,where p is a prime.If G is polycyclic-by-finite and the map φ:G→G defined by=g^φ,[g,a]is surjective,then G is soluble.If G is polycyclic,then CG(a^p)and G/[G,a^p]are both nilpotent-by-finite.展开更多
The concentration of carcinogenic polycyclic aromatic hydrocarbons （c-PAHs） present in the sediment and water of Peninsular Malaysia as well as in the cockle Anadara granosa was investigated. Samples were extracted ...The concentration of carcinogenic polycyclic aromatic hydrocarbons （c-PAHs） present in the sediment and water of Peninsular Malaysia as well as in the cockle Anadara granosa was investigated. Samples were extracted and analysed with gas chromatographymass spectrometry. The concentrations of total carcinogenic polycyclic aromatic hydrocarbons （t-PAHs） were measured between 0.80±0.04 to 162.96 ±14.74 ng/g wet weight （ww） in sediment, between 21.85± 2.18 to 76.2± 10.82 ng/L in water samples and between 3.34 ±0.77 to 46.85 ± 5.50 ng/g ww in the cockle tissue. The risk assessment of probable human carcinogens in the Group B2 PAHs was calculated and assessed in accordance with the standards of the United States Environmental Protection Agency （US EPA）. Case I in the toxicity assessment analysed the cancer risk to consumers of Malaysian blood cockle. Case II assessed the risk of cancer from exposure to PAHs from multiple pathways. The average cancer risk of case I and case II were found to be classifiable as unsafe according to the US EPA standard. The cancer risk due to c-PAHs acquired by the ingestion of blood cockle was （8.82 ± 0.54） × 10^ 6 to （2.67 ± 0.06） × 10^-2, higher than the US EPA risk management criterion. The non-cancer risks associated with multiple pathways in Kuala Gula, Kuala Juru and Kuala Perlis were higher than the US EPA safe level, but the non-cancer risk for eating blood cockle was below the level of US EPA concern.展开更多
Based on a general theory of descendant trees of finite p-groups and the virtual periodicity isomorphisms between the branches of a coclass subtree, the behavior of algebraic invariants of the tree vertices and their ...Based on a general theory of descendant trees of finite p-groups and the virtual periodicity isomorphisms between the branches of a coclass subtree, the behavior of algebraic invariants of the tree vertices and their automorphism groups under these isomorphisms is described with simple transformation laws. For the tree of finite 3-groups with elementary bicyclic commutator qu-otient, the information content of each coclass subtree with metabelian main-line is shown to be finite. As a striking novelty in this paper, evidence is provided of co-periodicity isomorphisms between coclass forests which reduce the information content of the entire metabelian skeleton and a significant part of non-metabelian vertices to a finite amount of data.展开更多
Let p be a prime. For any finite p-group G, the deep transfers T H,G ' : H / H ' → G ' / G " from the maximal subgroups H of index (G:H) = p in G to the derived subgroup G ' are introduced as an ...Let p be a prime. For any finite p-group G, the deep transfers T H,G ' : H / H ' → G ' / G " from the maximal subgroups H of index (G:H) = p in G to the derived subgroup G ' are introduced as an innovative tool for identifying G uniquely by means of the family of kernels ùd(G) =(ker(T H,G ')) (G: H) = p. For all finite 3-groups G of coclass cc(G) = 1, the family ùd(G) is determined explicitly. The results are applied to the Galois groups G =Gal(F3 (∞)/ F) of the Hilbert 3-class towers of all real quadratic fields F = Q(√d) with fundamental discriminants d > 1, 3-class group Cl3(F) □ C3 × C3, and total 3-principalization in each of their four unramified cyclic cubic extensions E/F. A systematic statistical evaluation is given for the complete range 1 d 7, and a few exceptional cases are pointed out for 1 d 8.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Supported by National Natural Science Foundation of China(Grant No.11371124)Youth Foundation of Hebei Educational Committee(Grant Nos.QN2016184 and F2015402033)Graduate Education Teaching Reform Foundation of Hebei University of Engineering(Grant No.161290140004)
文摘Let G be a polycyclic group and α a regular automorphism of order four of G. If the map φ: G→ G defined by g;= [g, α] is surjective, then the second derived group of G is contained in the centre of G. Abandoning the condition on surjectivity, we prove that C;（α;） and G/[G, α;] are both abelian-by-finite.
文摘The structure of groups in which many subgroups have a certain property X has been investigated for several choices of the property χ.In particular, groups whose non-normal subgroups are supersoluble are studied ia this paper. Moreover, groups with only finitely many normalizers of non-supersoluble groups are considered.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.11801129,11771129)the Natural Science Foundation of Hebei Province(No.A2019402211)+3 种基金the Program for Young Top Talent of Higher Learning Institutions of Hebei(No.BJ2018025)the Foundation of Handan(No.1723208068-5)the Excellent Young and Middle-Aged Innovative Team Program of Hubei(No.T201601)the New Century High-Level Talents Foundation of Hubei.
文摘Let G be a group,and let a be a regular automorphism of order p2 of G,where p is a prime.If G is polycyclic-by-finite and the map φ:G→G defined by=g^φ,[g,a]is surjective,then G is soluble.If G is polycyclic,then CG(a^p)and G/[G,a^p]are both nilpotent-by-finite.
基金supported by the MOSTI Science Funding Project(No. 5450100)
文摘The concentration of carcinogenic polycyclic aromatic hydrocarbons （c-PAHs） present in the sediment and water of Peninsular Malaysia as well as in the cockle Anadara granosa was investigated. Samples were extracted and analysed with gas chromatographymass spectrometry. The concentrations of total carcinogenic polycyclic aromatic hydrocarbons （t-PAHs） were measured between 0.80±0.04 to 162.96 ±14.74 ng/g wet weight （ww） in sediment, between 21.85± 2.18 to 76.2± 10.82 ng/L in water samples and between 3.34 ±0.77 to 46.85 ± 5.50 ng/g ww in the cockle tissue. The risk assessment of probable human carcinogens in the Group B2 PAHs was calculated and assessed in accordance with the standards of the United States Environmental Protection Agency （US EPA）. Case I in the toxicity assessment analysed the cancer risk to consumers of Malaysian blood cockle. Case II assessed the risk of cancer from exposure to PAHs from multiple pathways. The average cancer risk of case I and case II were found to be classifiable as unsafe according to the US EPA standard. The cancer risk due to c-PAHs acquired by the ingestion of blood cockle was （8.82 ± 0.54） × 10^ 6 to （2.67 ± 0.06） × 10^-2, higher than the US EPA risk management criterion. The non-cancer risks associated with multiple pathways in Kuala Gula, Kuala Juru and Kuala Perlis were higher than the US EPA safe level, but the non-cancer risk for eating blood cockle was below the level of US EPA concern.
文摘Based on a general theory of descendant trees of finite p-groups and the virtual periodicity isomorphisms between the branches of a coclass subtree, the behavior of algebraic invariants of the tree vertices and their automorphism groups under these isomorphisms is described with simple transformation laws. For the tree of finite 3-groups with elementary bicyclic commutator qu-otient, the information content of each coclass subtree with metabelian main-line is shown to be finite. As a striking novelty in this paper, evidence is provided of co-periodicity isomorphisms between coclass forests which reduce the information content of the entire metabelian skeleton and a significant part of non-metabelian vertices to a finite amount of data.
文摘Let p be a prime. For any finite p-group G, the deep transfers T H,G ' : H / H ' → G ' / G " from the maximal subgroups H of index (G:H) = p in G to the derived subgroup G ' are introduced as an innovative tool for identifying G uniquely by means of the family of kernels ùd(G) =(ker(T H,G ')) (G: H) = p. For all finite 3-groups G of coclass cc(G) = 1, the family ùd(G) is determined explicitly. The results are applied to the Galois groups G =Gal(F3 (∞)/ F) of the Hilbert 3-class towers of all real quadratic fields F = Q(√d) with fundamental discriminants d > 1, 3-class group Cl3(F) □ C3 × C3, and total 3-principalization in each of their four unramified cyclic cubic extensions E/F. A systematic statistical evaluation is given for the complete range 1 d 7, and a few exceptional cases are pointed out for 1 d 8.
