Hypocentral 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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This is a variation of nilpotence|Find other variations of nilpotence | Read a survey article on varying nilpotence
Definition
A group is said to be hypocentral if its lower central series terminates at the identity, or equivalently, if its hypocenter is the trivial group.
Relation with other properties
Stronger properties
- Nilpotent group: Here, the lower central series terminates at the identity in finitely many steps, the number of steps being the nilpotence class.
- Residually nilpotent group: Here, the intersection of the finite terms of the lower central series is the trivial group.