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The Isomorphism Problem of Normalized Unit Groups of Group Algebras of a Class of Finite 2-groups

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Acta Mathematica Sinica,English Series 2023年第11期39卷 2275-2282页

作者： yu lei wang He Guo LIU Department of Mathematics He’nan University of TechnologyZhengzhou 450001P.R.China Department of Mathematics Hainan UniversityHaikou 570228P.R.China

Let p be a prime and F_p be a finite field of p *** F_(pG)denote the group algebra of the finite p-group G over the field F_(p)and V(F_(pG))denote the group of normalized units in F_(pG).Suppose that G and H are finite p-groups given by a central extension of the form 1→Z_(p)^(m)→G→Z_(p)×···×Z_(p)→1 and G'≌Z_(p),m≥*** V(F_(p)G)≌V(F_(p)H)if and only if G≌*** and Bovdi only solved the isomorphism problem when p is *** this paper,the case p=2 is determined.

关键词： isomorphism problem normalized unit Frattini subgroup finite 2-group

A Class of Finite Resistant p-Groups

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Acta Mathematica Sinica,English Series 2017年第5期33卷 725-730页

作者： He Guo LIU yu lei wang Department of Mathematics Hubei University Department of Mathematics He'nan University of Technology

A finite p-group P is called resistant if, for any finite group G having P as a Sylow p-group,the normalizer N_G(P) controls p-fusion in G. Let P be a central extension as 1→ Z_(p^m)→ P→ Z_p × · · · × Z_p→1,a... 详细信息

关键词： Finite p-groups symplectic groups fused p-centric

Automorphisms of Extensions of Q by a Direct Sum of Finitely Many Copies of Q

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Acta Mathematica Sinica,English Series 2019年第2期35卷 204-212页

作者： He Guo LIU yu lei wang Ji Ping ZHANG Department of Mathematics Hubei University Department of Mathematics He'nan University of Technology The School of Mathematical Sciences Peking University

Let G be an extension of Q by a direct sum of r copies of Q.(1) If G is abelian, then G is a direct sum of r + 1 copies of Q and Aut G = GL(r + 1, Q);(2) If G is non-abelian, then G is a direct product of an extraspecial Q-group E and m copies of Q, where E/ζ E is a linear space over Q with dimension 2 n and m + 2 n = r. Furthermore, let Aut_G'G be the normal subgroup of Aut G consisting of all elements of Aut G which act trivially on the derived subgroup G of G, and Aut_(G/ζG),_(ζG)G be the normal subgroup of Aut G consisting of all central automorphisms of G which also act trivially on the center ζ G of G. Then(i) The extension 1→ Aut_(G')G→ Aut G→ Aut G'→ 1 is split;(ii)Aut_(G')G/Aut_(G/ζG),_(ζG)G = Sp(2 n, Q) ×(GL(m, Q) Q^(m));(iii) Aut_(G/ζG),ζGG/Inn G= Q^(2 nm).

关键词： Extraspecial Q-group group extension symplectic group automorphism group

The Automorphism Group of a Class of Nilpotent Groups with Infinite Cyclic Derived Subgroups

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Acta Mathematica Sinica,English Series 2018年第7期34卷 1151-1158页

作者： He Guo LIU yu lei wang Ji Ping ZHANG Department of Mathematics Hubei University Wuhan 430062 P. R. China Department of Mathematics Henan University of Technology Zhengzhou 450001 P. R. China The School of Mathematical Sciences Peking University Beijing 100871 P. R. China

The automorphism group of a class of nilpotent groups with infinite cyclic derived subgroups is determined. Let G be the direct product of a generalized extraspecial E-group E and a free abelian group A with rank m, where E={{1 kα1 kα2…kαn aα＋1 0 1 0 … 0 αn＋2 0 0 0 … 1 α2n＋1 0 0 0 …0 1}}αi∈Z,i=1,2,…,2n＋1},where k is a positive integer. Let AutG＇G be the normal subgroup of AutG consisting of all elements of AutG which act trivially on the derived subgroup G＇ of G, and Autc G/ζG,ζGG be the normal subgroup of AutG consisting of all central automorphisms of G which also act trivially on the center ζG of G. Then （i） The extension →AutG＇G→AutG→AutG＇→1 is split.（ii）AutG＇G/AutG/ζG,ζGG≈Sp（2n,Z）×（GL（m,Z）×（Z）m）,（iii）Aut GζG,ζGG/InnG≈（Zk）2n＋（Z）2nm.

关键词： Generalized extraspecial Z-group symplectic group automorphism group

A Class of Finite Groups with Complete Character Degree Graphs

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Acta Mathematica Sinica,English Series 2013年第11期29卷 2155-2158页

作者： Qing yun MENG Xiao You CHEN yu lei wang College of Science He’nan University of Technology

In this paper, we construct a new class of finite groups whose common divisor graphs are complete graphs, while there is no prime dividing all the nontrivial degrees.

关键词： Finite group character degree character degree graph

Micro-analysis of high-temperature oxidation-resistance of a new kind of heat-resistant grid plate in grate-kiln

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International Journal of Minerals,Metallurgy and Materials 2009年第6期16卷 632-639页

作者： Jun-you Liu Feng Li Jie Liu Yi Zhang yu-lei wang School of Materials Science and Engineering University of Science and Technology Beijing Beijing 100083 China Beijing BKDR Metallurgy Engineering ＆ Technology Co. Ltd. Beijing 100083 China

To further improve the oxidation-resistance of materials and reduce the cost of grid plates in grate-kiln, a new kind of heat-resistant grid plate was developed. The microstructure of this grid plate with a life more than 18 months was studied by XRD, SEM and EDS techniques. The results show that high hardness, high intensity and good impact property make the new kind of heat-resistant grid plate and its oxide film have a higher resistance to deformation and abrasion at 900-1000℃ Besides, small grain size is beneficial to form a complete protective oxide film. The oxide film composed of SiO2 layer, Cr2O3 layer and Fe2O3 layer is rather thin and bonds closely with the backing. The forming of the chemical stable nickel-rich layer increases the density of Cr2O3 layer.

关键词： grate-kiln process grid plate heat resistance high-temperature oxidation-resistance oxide film

Relationship between preoperative staging by endoscopic ultrasonography and MMP-9 expression in gastric carcinoma

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World Journal of Gastroenterology 2007年第14期13卷 2108-2112页

作者： Shi-yun Tan Jun-yu wang lei Shen He-Sheng Luo Zhi-Xiang Shen Department of Gastroenterology Renmin Hospital Wuhan University Wuhan 430060 Hubei Province China

AIM: To investigate the relationship between the staging by endoscopic ultrasonography (EUS) and the expression of carcinoma metastasis associated gene in the patients with gastric carcinoma. METHODS: Sixty-three patients with gastric cancer were diagnosed by electric gastroscopy and EUS. The preoperative staging of gastric cancer was measured by EUS and compared with pathologic staging and MMP-9 expression. Peripheral serum level of MMP-9 was measured with enzyme-linked immunosorbent assay (ELISA), while the expression of MMP-9 protein was tested with immunohistochemistry and hybridization in situ in the gastric carcinoma tissues. RESULTS: The total accuracy of EUS in estimating invasive depth of gastric cancer was 80.95%, while that in estimating lymphatic metastasis was 73.02%. Serum MMP-9 levels were consistent with the expression of MMP-9 protein and MMP-9 mRNA in tissue, a result closely correlated with invasive degree, staging with EUS and lymphatic metastasis in gastric cancer (P < 0.05). The total accuracy of estimating invasive depth in gastric cancer was 95.22% using both EUS and MMP-9. CONCLUSION: The MMP-9 level of preoperative serum presents the reference value for preoperative staging by EUS in the patients with gastric cancer. When serum MMP-9 level in gastric cancer is significantly high, physicians should pay closer attention to the metastasis which reaches the serosa or beyond. Combining EUS and MMP-9 improves the accuracy in deciding the invasion and metastasis in the patients with gastric carcinoma.

关键词： Endoscopic ultrasonography Stomachneoplasm Gastroscopy Neoplasm staging Matrixmetalloproteimase 9

Carbon Dioxide Captured from Flue Gas by Modified Ca-based Sorbents in Fixed-bed Reactor at High Temperature

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Chinese Journal of Chemical Engineering 2013年第2期21卷 199-204页

作者： YANG lei yu Hongbing wang Shengqiang wang Haowen ZHOU Qibin College of Environmental Science and Engineering Nankai University Tianjin 300071 China

Four kinds of Ca-based sorbents were prepared by calcination and hydration reactions using different precursors： calcium hydroxide, calcium carbonate, calcium acetate monohydrate and calcium oxide. The CO2 absorption capacity of those sorbents was investigated in a fixed-bed reactor in the temperature range of 350-650 ℃. It was found that all of those sorbents showed higher capacity for CO2 absorption when the operating temperature higher than 450 ℃. The CaAc2-CaO sorbent showed the highest CO2 absorption capacity of 299 mg.g-1. The mor- phology of those sorbents was examined by scanning electron microscope （SEM）, and the changes of composition before and after carbonation were also determined by X-ray diffraction （XRD）. Results indicated that those sorbents have the similar chemical compositions and crystalline phases before carbonation reaction [mainly Ca（OH）2], and CaCO3 is the main component after carbonation reaction. The SEM morphology shows clearly that the sorbent pores were filled with reaction products after carbonation reaction, and became much denser than before. The N2 adsorption-desorption isotherms indicated that the CaAc2-CaO and CaCO3-CaO sorbents have higher specific surface area. lar2er oore volume and anoropriate pore size distribution than that of CaO-CaO and Ca（OH）2-CaO.

关键词： CO2 capture carbonation reaction fixed-bed reactor multicycle reaction

The entropy weight fuzzy comprehension evaluation of enterprise knowledge competitiveness

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Chinese Business Review 2010年第2期9卷 46-50页

作者： yu lei wang Shu-zhen Department of Business Agriculture University of Hebei Baoding 071001 China

With the constant development of knowledge-based economy, knowledge has become the core competitiveness of enterprise, which plays a vital role in the development of enterprise and market competition. It will be helpful for enterprise managers to improve their knowledge competitiveness, if they can judge the advantage and disadvantage of knowledge competitiveness reasonably. According to the nature and the characteristic of knowledge competitiveness of enterprise, a system of evaluation index has been designed about the knowledge competitiveness of enterprise. Taking the enterprise A as an example, it is appraised by using fuzzy comprehension evaluation based on entropy weight, and has provided a new idea for the knowledge competitiveness of enterprise.

关键词： knowledge competitiveness entropy weight fuzzy comprehension evaluation