Group in which every finite subgroup is cyclic

Symbol-free definition
A group in which every finite subgroup is cyclic is a group where every subgroup that is finite, is cyclic as a group: it is generated by one element. In other words, every fact about::finite subgroup is a fact about::cyclic subgroup.

Stronger properties

 * Weaker than::Locally cyclic group
 * Weaker than::Multiplicative group of a field
 * Weaker than::Group with at most n elements of order dividing n

Weaker properties

 * Stronger than::Group in which every finite abelian subgroup is cyclic

Metaproperties
If $$G$$ is a group in which every finite subgroup is cyclic, and $$H$$ is a subgroup of $$G$$, then every finite subgroup of $$H$$ is also cyclic.