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 C_G(g), then:

C_G 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 C_G(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 C_G(g).

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

It is true that C_G(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

Kuru Kuru Kururin

... Kuru Kururin is a game for the Game Boy Advance. The player controls a slowly spinning stick and must get it through a series of mazes without touching the walls ...