Group in which elements of coprime finite orders commute

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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 elements of coprime finite orders commute is a group in which any two elements, both of which have finite orders such that the orders are relatively prime to others, must commute.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
nilpotent group |FULL LIST, MORE INFO
locally nilpotent group every finitely generated subgroup is nilpotent |FULL LIST, MORE INFO
group in which order of commutator divides order of element |FULL LIST, MORE INFO

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
group in which every finite subgroup is nilpotent |FULL LIST, MORE INFO