---
tag: N2KNP4292N
kind: concept
name: Absolutely simple group
sources:
  - wikipedia: en:4966802@r1268644027
    locator: Absolutely simple group
    note: adopted
    mention: wikipedia://en/4966802
    sections: [Summary]
same_as:
  wikidata: Q4669869
  wikipedia: Absolutely simple group
inventory: [7G9MP24FFR]
---

## Summary

In mathematics, in the field of group theory, a group is said to be **absolutely simple** if it has no proper nontrivial serial subgroups. That is, $G$ is an absolutely simple group if the only serial subgroups of $G$ are $\{ e \}$ (the trivial subgroup), and $G$ itself (the whole group).