Unicentral 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 unicentral if its epicenter equals its center, or equivalently, the only central subgroup for which the quotient group is a capable group is the whole center.

Relation with other properties

Stronger properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
epabelian group	abelian and unicentral			|FULL LIST, MORE INFO
centerless group	center is trivial			|FULL LIST, MORE INFO