Group in which every periodic subgroup is locally finite

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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 in which every periodic subgroup is locally finite is a group satisfying the following equivalent conditions:

  1. Every perodic subgroup of the group is locally finite
  2. Every finitely generated periodic subgroup of the group is finite

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
group in which every periodic subgroup is finite
abelian group follows from equivalence of definitions of periodic abelian group
nilpotent group follows from equivalence of definitions of periodic nilpotent group