# The regular semisimple element in the algebraic group

Suppose some maximal torus $T$ of $G$ is $C_G(T)$, then the set of semisimple elements for which $C_G(s)$ is a torus contains a nonempty open set. Such element are called regular semisimple.

I want to know how to prove this claim and want to find some good examples for some common algebraic groups such as $\mathrm{SL}(n,K)$.

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If $K$ in the question is algebraically closed then any semisimple element $s$ can be diagonalized; it is regular if and only if all eigenvalues are distinct. This is equivalent, as Turgeon refers to Borel's book, to being outside the kernel of every root. –  Abhishek Parab Jun 27 at 15:50