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locally finite group
In mathematics, in the field of group theory, a locally finite group is a type of group that can be studied in ways analogous to a finite group. Sylow subgroups, Carter subgroups, and abelian subgroups of locally finite groups have been studied.
==Definition and first consequences==
A locally finite group is a group for which every finitely generated subgroup is finite.
Since the cyclic subgroups of a locally finite group are finite, every element has finite order, and so the group is periodic.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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