Sims conjecture

In mathematics, the Sims conjecture is a result in group theory, originally proposed by Charles Sims. He conjectured that if formula_1 is a primitive permutation group on a finite set formula_2 and formula_3 denotes the stabilizer of the point formula_4 in formula_2, then there exists an integer-valued function formula_6 such that formula_7 for formula_8 the length of any orbit of formula_3 in the set formula_10. 
The conjecture was proven by Peter Cameron, Cheryl Praeger, Jan Saxl, and Gary Seitz using the classification of finite simple groups, in particular the fact that only finitely many isomorphism types of sporadic groups exist. A consequence of their proof is that there exist only finitely many connected distance-transitive graphs having degree greater than 2.