Locally FZ-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 a locally FZ-group if it satisfies the following equivalent conditions:
- Every finitely generated subgroup is a finitely generated FZ-group
- Every finitely generated subgroup is a FZ-group.
Relation with other properties
Stronger properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| FZ-group | the inner automorphism group is a finite group | |FULL LIST, MORE INFO | ||
| group with finite derived subgroup | the derived subgroup is a finite group | |FULL LIST, MORE INFO | ||
| FC-group | every conjugacy class is finite. | |FULL LIST, MORE INFO | ||
| locally finite group | every finitely generated subgroup is finite | |FULL LIST, MORE INFO | ||
| finite group | underlying set is finite | |FULL LIST, MORE INFO |