Encyclopedia > Talk:Conjugacy class

  Article Content

Talk:Conjugacy class

Reverting to previous text , as the centralizer is indeed a subgroup of G; if a,b in CG(g), then:

  • CG is not empty, since (g*g)*g = g*(g*g).
  • b * g = g * b → b -1 * g = g * b -1; thus b -1 is in CG(g)
  • (a*b -1)*g = a*(b -1*g) = a*(g*b -1) = (a*g)*b -1 = (g*a)*b -1 = g*(a*b -1) → a*b -1 in CG(g).

thus by elementary group theory, CG(g) is a subgroup of G.

It is true that CG(g) is not a normal subgroup of G; but that's not what was stated in the article. Maybe this should be added to the article.User:chas_zzz_brown



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
Quadratic formula

... trinomial of the form x2 + 2xy + y2. Since "2xy" in this case is (b/a)x, we must have y = b/(2a), so we add the square of b/(2a) to both sides, ...

 
 
 
This page was created in 30.8 ms