Exchange环的K0群的正向凸子群格

本文证明了：(1)Exchange环R的K0群的正向凸子群格同构于R的稳定余有限半本原理想格；(2)稳定有限、半本原的exchange环R是单的当且仅当它是K0-单的并且满足逼近弱s^*—可比性，推广了Goodearl，Ara等人的结果。     

Segal－Bargmann－Hall Transform and Geometric Quantization

Using geometric methods, Hall has proved that the Segal-Bargmann transform for a con-nected Lie group K of compact type is an isometric isomorphism [H1] and is unique when Kis simply connected [H7]. Furthermore, Hall considered geometric quantization of T~*(K), K'scotangent bundle [H9]. Using the vertical polarization and a natural Khler polarization obtainedby identifying T~*(K) with the complexified group KC, Hall concluded that the pairing map be-tween the two Hilbert Spaces induced by these two polarizations coincides with the generalizedSegal-Bargmann transform C_t (up to constant).     

On the p—Local Rank of Finite Groups

In this paper,we shall mainly study the p-solvable finite group in terms of p-local rank,and a group theoretic characterization will be given of finite p-solvabel groups with p-local rank two.Theorem A Let G be a finite p-solvable group with p-local rank plr(G)=2 and Op(G)=1.If P is a Sylow p-subgrounp of G,then P has a normal subgroup Q such that P/Q is cyclic or a generalized quaternion 2-group and the p-rank of Q is at most two.Theorem B Let G be a finite p-solvable group with Op(G)=1.Then the p-length lp(G)≤plr(G);if in addition plr(G)=lp (G) and p≥5 is odd,then plr(G)=0 or 1.     

弱SS-半置换性极小子群对有限群超可解性的影响

引入弱SS-半置换子群的概念,介绍了弱SS-半置换子群的性质,结合有限群G的极小于群的弱SS-半置换性,并结合C-正规性来讨论有限群的超可解性及幂零性,得到了有限群超可解及幂零的若干充分或充要条件,同时推广了某些著名结果.     

Geometric Characterizations for Subgroups of PU（1, n; C）

In this paper, we discuss non-elementary subgroups and discontinuous subgroups of PU(1,n; C), and give their geometric characterizations.     

Dubrovin赋值斜群环

本文中对一个斜群环为Dubrovin赋值环给出了一系列等价刻画,并且刻画了一个Dubrovin赋值斜群环的所有素理想.     

Hall广义补和群的可解性

研究具有某些特殊性质的广义补,得到了一些可解性的判别条件.如果对G的任意Sylow p-子群P,p∈{2,3}∩丌(G),NG(P)在G中都存在广义补H使H/D是G/D的Hall子群且H/D为幂零群,其中D=(H∩ⅣG(P))G,那么G可解.     

具有较少非循环子群共轭类的有限群

设G是有限群,用δ(G)表示群G的非循环子群的共轭类数,πr(G)表示整除|G|的素因子的集合.本文主要研究满足条件δ(G)≤|π(G)|+1的有限群,得到这类群可解,并给出它们的同构分类进一步证明,δ(G)=|π(G)|+2的有限非可解群必同构于A_5或SL(2,5).     

A Generalization about Congruent Pairs on a Set

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