Sims conjecture

Statement

In mathematics, the Sims conjecture is a result in group theory, originally proposed by Charles Sims. He conjectured that if $G$ is a primitive permutation group on a finite set $S$ and $G_\alpha$ denotes the stabilizer of the point $\alpha$ in $S$, then there exists an integer-valued function $f$ such that $f(d) \geq |G_\alpha|$ for $d$ the length of any orbit of $G_\alpha$ in the set $S \setminus \{\alpha\}$.