Locally finite group

This is a variation of finiteness (groups)|Find other variations of finiteness (groups) |

Definition

Symbol-free definition

A group is said to be locally finite if every subgroup of it that is finitely generated, is in fact finite.

Definition with symbols

A group $G$ is said to be locally finite if for any finite subset $g_{1}, g_{2}, \dots, g_{n} \in G$ the group generated by the $g_{i}$ s is a finite group.

Formalisms

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In terms of the locally operator

This property is obtained by applying the locally operator to the property: finite group
View other properties obtained by applying the locally operator

Relation with other properties

Stronger properties

Finite group