# 2-locally finite 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 $G$ is termed a 2-locally finite group if, given any two elements $g_1, g_2 \in G$, the subgroup $\langle g_1, g_2 \rangle$ is a finite group.

## Relation with other properties

### Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
locally finite group every finitely generated subgroup is finite (direct) Follows from Golod's theorem on locally finite groups |FULL LIST, MORE INFO

### Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions