Talk:Center (group theory)

Z(G)
Why is the center always written as Z(G)? Z comes from the German zentrum or zahlen (integer)? Albmont (talk) 17:24, 24 March 2009 (UTC)


 * It comes from Zentrum (see also de:Zentrum (Algebra)). In German, the centralizer is also denoted by Z, as in de:Zentralisator.  Sometimes in English, the center is denoted C = CG(G), but Z = Z(G) is much more common. JackSchmidt (talk) 17:49, 24 March 2009 (UTC)

Is it true that c-1ZG(S)c=ZG(c-1Sc)
Is it true that c-1ZG(S)c = ZG(c-1Sc) where G is the group and S is some subset of the group and c is a fixed element of G.

Note that c-1Sc = (c-1)b(c) where b is in S and (c-1) is inverse of c. And ZG(c-1Sc) = (c-1)b(c) for b in ZG(S). Mind that here the two b's are not the same!

If it is so then I think it should be mentioned in the article along with giving its proof, with a few examples at the end. — Preceding unsigned comment added by 173.206.28.213 (talk) 04:47, 7 June 2011 (UTC)

Question
Why is field is necessary for the group & vector space?? Muhammad Arfan Jutt (talk) 07:55, 2 April 2018 (UTC)

Section on application?
I think it would be good to have a short section on the applications of the concept of a center. Zaunlen (talk) 15:17, 10 November 2019 (UTC)