Metanilpotent group

This article is about a standard (though not very rudimentary) definition in group theory. The article text may, however, contain more than just the basic definition
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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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Definition

A group is termed metanilpotent if it has a nilpotent normal subgroup (i.e., a normal subgroup that is nilpotent as a group) such that the quotient group is also a nilpotent group.

Relation with other properties

Stronger properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
Nilpotent group
Abelian group
Metabelian group
Metacyclic group

Weaker properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
Solvable group