Abstract
Abstract We prove that if 𝐺 is a connected semisimple algebraic group of rank 𝑟, and 𝐻 is a subgroup of 𝐺 that is contained in no proper parabolic subgroup, then we have | C G ( H ) | < c r | Z ( G ) | \lvert C_{G}(H)\rvert<c^{r}\lvert Z(G)\rvert , where 𝑐 is an absolute constant ( c = 16 c=16 if all simple factors of 𝐺 are classical, and c ≤ 197 c\leq 197 in general).
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