---
tag: CE798H4KZ8
kind: statement
role: proposition
name: Sims conjecture
sources:
  - wikipedia: en:60436463@r1240488300
    locator: Sims conjecture
    note: adopted
    mention: wikipedia://en/60436463
    sections: [Statement]
same_as:
  wikidata: Q65063913
  wikipedia: Sims conjecture
inventory: [SJDAAMD12G]
---

## 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|0C4JS9RF5M]]-valued [[function|0EPAT51DXQ]] $f$ such that $f(d) \geq |G_\alpha|$ for $d$ the length of any orbit of $G_\alpha$ in the set $S \setminus \{\alpha\}$.