Virtually nilpotent 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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Definition

A group is termed virtually nilpotent if it satisfies the following equivalent conditions:

1. It has a subgroup of finite index that is nilpotent.
2. It has a normal subgroup of finite index that is nilpotent.
3. There is a surjective homomorphism from it to a finite group such that the kernel is a nilpotent normal subgroup.
4. There is a homomorphism from it to a finite group such that the kernel is a nilpotent normal subgroup.

Formalisms

In terms of the virtually operator

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

Relation with other properties

Stronger properties

• Virtually abelian group

Weaker properties

• Virtually solvable group