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
Objective: To investigate the effects of composite Sophora colon-soluble Capsule(CSCC) on gut microbiota-mediated short-chain fatty acids(SCFAs) production and downstream group 3 innate lymphoid cells(ILC3s) of dextra...Objective: To investigate the effects of composite Sophora colon-soluble Capsule(CSCC) on gut microbiota-mediated short-chain fatty acids(SCFAs) production and downstream group 3 innate lymphoid cells(ILC3s) of dextran sulfate sodium(DSS)-induced ulcerative colitis(UC) mice model. Methods: The main components of CSCC were analyzed by hybrid ultra-high-performance liquid chromatography ion mobility spectromety quadrupole time-of-flight mass spectrometry(UHPLC-IM-QTOF/MS). Twenty-four male BALB/c mice were randomly divided into 4 groups(n=6) by using a computer algorithm-generated random digital, including control, DSS model, mesalazine, and CSCC groups. A DSS-induced colitis mice model was established to determine the effects of CSCC by recording colonic weight, colonic length, index of colonic weight, and histological colonic score. The variations in ILC3s were assessed by immunofluorescence and flow cytometry. The results of gut microbiota and SCFAs were acquired by 16s r DNA and gas chromatography-mass spectrometry(GC-MS) analysis. The expression levels of NCR^(+)ILC3^(-), CCR6^(+)Nkp46-(Lti) ILC3^(-), and ILCreg-specific markers were detected by enzyme-linked immunosorbent assay, and real-time quantitative polymerase chain reaction and Western blot, respectively. Results: The main components of CSCC were matrine, ammothamnine, Sophora flavescens neoalcohol J, and Sophora oxytol U. After 7 days of treatment, CSCC significantly alleviated colitis by promoting the reproduction of intestinal probiotics manifested as upregulation of the abundance of Bacteroidetes species and specifically the Bacteroidales_S24-7 genus(P<0.05). Among the SCFAs, the content of butyric acid increased the most after CSCC treatment. Meanwhile, compared with the model group, Lti ILC3s and its biomarkers were significantly downregulated and NCR^(+) ILC3s were significantly elevated in the CSCC group(P<0.01). Further experiments revealed that ILC3s were differentiated from Lti ILC3s to NCR^(+)ILC3s, resulting in interleukin-22 production wh展开更多
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
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
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Supported by the National Natural Science Foundation of China (No.81673965)Beijing Natural Science Foundation (No.7224362)。
文摘Objective: To investigate the effects of composite Sophora colon-soluble Capsule(CSCC) on gut microbiota-mediated short-chain fatty acids(SCFAs) production and downstream group 3 innate lymphoid cells(ILC3s) of dextran sulfate sodium(DSS)-induced ulcerative colitis(UC) mice model. Methods: The main components of CSCC were analyzed by hybrid ultra-high-performance liquid chromatography ion mobility spectromety quadrupole time-of-flight mass spectrometry(UHPLC-IM-QTOF/MS). Twenty-four male BALB/c mice were randomly divided into 4 groups(n=6) by using a computer algorithm-generated random digital, including control, DSS model, mesalazine, and CSCC groups. A DSS-induced colitis mice model was established to determine the effects of CSCC by recording colonic weight, colonic length, index of colonic weight, and histological colonic score. The variations in ILC3s were assessed by immunofluorescence and flow cytometry. The results of gut microbiota and SCFAs were acquired by 16s r DNA and gas chromatography-mass spectrometry(GC-MS) analysis. The expression levels of NCR^(+)ILC3^(-), CCR6^(+)Nkp46-(Lti) ILC3^(-), and ILCreg-specific markers were detected by enzyme-linked immunosorbent assay, and real-time quantitative polymerase chain reaction and Western blot, respectively. Results: The main components of CSCC were matrine, ammothamnine, Sophora flavescens neoalcohol J, and Sophora oxytol U. After 7 days of treatment, CSCC significantly alleviated colitis by promoting the reproduction of intestinal probiotics manifested as upregulation of the abundance of Bacteroidetes species and specifically the Bacteroidales_S24-7 genus(P<0.05). Among the SCFAs, the content of butyric acid increased the most after CSCC treatment. Meanwhile, compared with the model group, Lti ILC3s and its biomarkers were significantly downregulated and NCR^(+) ILC3s were significantly elevated in the CSCC group(P<0.01). Further experiments revealed that ILC3s were differentiated from Lti ILC3s to NCR^(+)ILC3s, resulting in interleukin-22 production wh
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.
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.
