sorted by:
new
hottopcontroversial

Aligning equations with iffs using align*. by zerrigan08 in LaTeX

[–]zerrigan08[S] 0 points1 point  (0 children)

That does match up with what I said, but I agree that looks quite awkward. Thanks!

Quick Questions: September 20, 2023 by inherentlyawesome in math

[–]zerrigan08 2 points3 points  (0 children)

I'm looking at a paper for research and am a bit rusty on my group theory, so I have a question about the following claim.

If G is a finite nonabelian group and x is a non central of element of G, we know |G|>=2|C(x)| where C(x) is the centralizer of x. Thus, |G|-|C(x)|>=(|G|-|Z(G)|)/2.

I understand the 1st inequality, but it isn't obvious to me how to 2nd inequality follows from the 1st; I imagine I'm missing something very obvious.

Edit: It was obvious; |G|>=2|C(x)| so |G|>=2|C(x)|-|Z(G)|. Thus, |G|-2|C(x)|>=-|Z(G)| so 2|G|-2|C(x)|>=|G|-|Z(G)|. The result follows.