请输入您要查询的字词:

 

单词 FaithfulGroupAction
释义

faithful group action


Let A be a G-set, that is, a set acted upon by a group G with actionψ:G×AA. Then for any gG, the map mg:AA defined by

mg(x)=ψ(g,x)

is a permutation of A (in other words, a bijective function from A to itself) and so an element of SA.We can even get an homomorphismPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath from G to SA by the rule gmg.

If for any pair g,hG gh we havemgmh, in other words, the homomorphism gmg being injectivePlanetmathPlanetmath, we say that the action is faithfulPlanetmathPlanetmath.

随便看

 

数学辞典收录了18232条数学词条,基本涵盖了常用数学知识及数学英语单词词组的翻译及用法,是数学学习的有利工具。

 

Copyright © 2000-2023 Newdu.com.com All Rights Reserved
更新时间:2025/5/4 22:01:31