Locally FZ-group

From Groupprops
Jump to: navigation, search
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

Definition

A group is termed a locally FZ-group if it satisfies the following equivalent conditions:

  1. Every finitely generated subgroup is a finitely generated FZ-group
  2. 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 Group with finite derived subgroup|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 Group with finite derived subgroup|FULL LIST, MORE INFO