Contents Generalized Simple Groups of Lin Type Chen Chen Hu (Chen Zhongghu) 1 Abstract Group Theory Z.M.Chen 4 Several Questions About Finite Group Representations and Their Applications Fan Yun 31 Recent Progress on Classical Groups and Algebraic K Theory in China Li Fu-an and You Hong 41 Some Work on the Connection Between Groups and Combinatorics Li Huiling 57 On the Subgroup Structure of Classical Groups Shangzhi Li 70 Complex Lie Algebra in China Lu Caihui, Zhang Hechun and Zhao Kaiming 91 Lie Algebras of Prime C.haracteristic Guang-Yu Shen 116 Left Cells in Certain Coxeter Groups Jian-yi Shi 130 Some Works on Modular Representations of Finite Groups Shi Shengming and Zhang Jiping 149 The Quantitative Structure of Groups and Related Topics W J.Shi 163 Survey on Geometry of Classical Groups over Finite Fields and Its Applications Zhe-xian Wan 182 Representation Theory of Algebraic and Quantum Groups in China Jianpan Wang and Jiachen Ye 203 Some Work on Vertex-Transitive Graphs by Chinese Mathematicians Ming-Yao Xu 224 Some New Developments in the Study of Differential Geometry of Homogeneous Spaces Yan Zhida and Hou Zixin 255