Hypercentral 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
View a complete list of group properties
VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions
This is a variation of nilpotence|Find other variations of nilpotence | Read a survey article on varying nilpotence

Definition

Symbol-free definition

A group is said to be hypercentral (also, hypernilpotent) if its upper central series terminates at the whole group, or equivalently, if it equals its hypercenter.

Relation with other properties

Stronger properties

Weaker properties