Virtually abelian group

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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