A group is locally finite when every subgroup that is a finitely generated group is finite. It is a torsion group, since the cyclic subgroup generated by one element must be finite. A restricted direct sum of groups with finite factors is locally finite. A locally finite group can be infinite, while a locally finite finitely generated group is finite by definition.
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A **locally finite group** is a type of group in the field of abstract algebra. Specifically, a group \( G \) is called locally finite if every finite subset of \( G \) generates a finite subgroup of \( G \). In other words, for any finite subset \( S \) of \( G \), the subgroup generated by \( S \), denoted by \( \langle S \rangle \), is finite.