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
periodic group	every element has finite order			|FULL LIST, MORE INFO
group generated by periodic elements	the group has a generating set in which every element has finite order			|FULL LIST, MORE INFO