---
tag: 6DAQYANC0Y
kind: concept
name: Virtually
aliases: [virtually-abelian, virtually-abelian-group, virtually-free, virtually-free-group, virtually-nilpotent, virtually-nilpotent-group]
sources:
  - wikipedia: en:10377971@r1250818690
    locator: Virtually
    note: adopted
    mention: wikipedia://en/10377971
    sections: [Summary]
same_as:
  wikidata: Q7935201
  wikipedia: Virtually
inventory: [3KK3MB8BRX]
---

## Summary

In mathematics, especially in the area of abstract algebra that studies infinite groups, the adverb **virtually** is used to modify a property so that it need only hold for a [[subgroup|0X1JXT47GA]] of finite [[index|0DTXBQPA2S]]. Given a property P, the group *G* is said to be *virtually P* if there is a finite index subgroup $H \le G$ such that *H* has property P.