Normality of group schemes

Question

I am interested in calculating etale cohomology of group schemes. It would be useful to know when certain group schemes are normal, i.e., when their local rings at every point are integrally closed domains. In particular, I am curious about which of the following group schemes are normal: (i) $\text{GL}_n$, (ii) $\text{SL}_n$, and (iii) $\mu_p$ for $p$ prime.