Encyclopedia > Simple group

  Article Content

Simple group

A simple group is a mathematical group G which has more than one element and does not have any normal subgroups besides {e} (e being the identity element of G) and G itself.

Despite the name, simple groups are far from "simple". The finite simple groups are important because in a certain sense they are the "basic building blocks" of all finite groups, somewhat similar to the way prime numbers are the basic building blocks of the integers. This is expressed by the Jordan-Hölder theorem[?].

The only simple groups which are abelian are the cyclic groups whose order is a prime number. In a huge collaborative effort, the classification of finite simple groups was accomplished in 1982.



All Wikipedia text is available under the terms of the GNU Free Documentation License

 
  Search Encyclopedia

Search over one million articles, find something about almost anything!
 
 
  
  Featured Article
East Farmingdale, New York

... for females. The per capita income for the town is $25,466. 7.0% of the population and 4.6% of families are below the poverty line. Out of the total people living in ...

 
 
 
This page was created in 38.3 ms