以群的非空子集为元素的群

本文得到以下的结论:1.在G是有限群时,A是G的某一子群的商群。2.在G是无限群时,我们构造出A不是G的任何子群的商群的例子。3.A是G的商群的充要条件是:(ⅰ) (?)g∈G,存在A∈A,使得g∈A;(ⅱ)(?)A、B∈A,若A≠B,则A∩B=φ。     

关于正规p-补的一个定理

本文削弱了《内-外-∑群与极小非∑群》(陈重穆)一文中定理10.10A:条件而得到相同的结果,即定理 设G是有限群,p是|G|的素因子,且对|G|的任一素因子q有p(?)q-1 ),P是G的p-Sylow子群.若对于P的任一非平凡循环子群P,N_G(P)与C_G(P)都有正规p-补,则G为p-幂零群.     

A_5的一个新刻划与有限质元群

本文仅用“群的阶”、“元的阶”来刻划60阶单群A_5~-,即A_5~-的特征性质是:(1)群的阶至少含三个相异的质因子;(2)群中异于1的每元的阶均为质数.此外,本文还得出有限质元群的下述分类:1)q~n阶群;2)pq~n阶群;3)A_5~-.     

Monoidal 群的一个结构定理

群Ｇ称为ｍｏｎｏｉｄａｌ群，如果对于Ｇ的任一非空子集Ｓ，由Ｓ＾２＝｛ｓ１，ｓ２｜ｓｉ∈Ｓ｝＝Ｓ可推出１Ｇ∈Ｓ，这里１Ｇ是Ｇ的单位元。本文证明ｍｏｎｏｉｄａｌ群Ｇ具有正规列ＩＧ△Ｆ△Ｃ△Ｍ△Ｇ，其因子群具有给定的性质。     

A Tentative Analysis of the Use of Potential by Commercial Bank in Controlling Credit Scale

This article brings forward the conception of potential and filed potential in bank＇s competition under the inspiration of law of electric current in electrodynamics. It discusses the impact of potential shifting on commercial bank＇s credit scale and builds up a model for commercial bank to control the scale by credit pricing and risk policy in a dynamic way, and also gives some advice to domestic commercial bank for improving loan business, aiming to settle down the existing credit management problems.