---
tag: 9RKBC8G3Z1
kind: concept
name: Block (permutation group theory)
sources:
  - wikipedia: en:3769397@r1352615709
    locator: Block (permutation group theory)
    note: adopted
    mention: wikipedia://en/3769397
    sections: [Summary]
same_as:
  wikidata: Q4927124
  wikipedia: Block (permutation group theory)
inventory: [7TKABEMEVN]
---

## Summary

In mathematics and group theory, a **block** for the action of a group $G$ on a [[set|0BSJ7RQ9BW]] $X$ is a subset $Y$ of $X$ whose images under $G$ either coincide with $Y$ or are disjoint from $Y$. These images form a **block system**, a partition of $X$ that is $G$-invariant. In terms of the associated [[equivalence relation|0G8VEZ3WTK]] on $X$, $G$-invariance means that