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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A group is termed virtually nilpotent if it satisfies the following equivalent conditions:
- It has a subgroup of finite index that is nilpotent.
- It has a normal subgroup of finite index that is nilpotent.
- There is a surjective homomorphism from it to a finite group such that the kernel is a nilpotent normal subgroup.
- There is a homomorphism from it to a finite group such that the kernel is a nilpotent normal subgroup.
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