2-locally finite group

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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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VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

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