Encyclopedia > Normal subgroup

  Article Content

Normal subgroup

In mathematics, a normal subgroup N of a group G is a subgroup invariant under conjugation; that is, for each element x in N and each g in G, the element g-1 x g is still in N.

Another way to put this is saying that right and left cosets of N in G coincide:

N g = g g-1 N g = g N    for all g in G.

Normal subgroups are of relevance because if N is normal, then the factor group G/N may be formed. Normal subgroups of G are precisely the kernels of group homomorphisms f : G -> H.

{e} and G are always normal subgroups of G. If these are the only ones, then G is said to be simple.



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
List of intelligence agencies

... (OGPU, 1923-1934) Narodnyi Kommissariat Gosudarstvennoi Bezopastnosti[?] (NKVD, 1934-1943) Ministerstvo Gosudarstvennoi Bezopastnosti[?] (MGB, 1946-1954) Komitet ...

 
 
 
This page was created in 51 ms