# Virtually abelian group

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions
This is a variation of Abelianness|Find other variations of Abelianness |

## Definition

### Symbol-free definition

A group is said to be virtually Abelian if it has an Abelian subgroup of finite index.

## Formalisms

### In terms of the virtually operator

This property is obtained by applying the virtually operator to the property: Abelian group
View other properties obtained by applying the virtually operator

## Relation with other properties

### Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
finite group
abelian group
FZ-group center is a subgroup of finite index FZ implies virtually abelian
locally finite linear group over characteristic zero
metacyclic group