Hypercentral 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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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
- Locally nilpotent group
- Group in which every maximal subgroup is normal
- Hyperabelian group