Unicentral 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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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