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・ Locallife
・ Locally acyclic morphism
・ Locally catenative sequence
・ Locally compact field
・ Locally compact group
・ Locally compact quantum group
・ Locally compact space
・ Locally connected space
・ Locally constant function
・ Locally convex topological vector space
・ Locally cyclic group
・ Locally decodable code
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・ Locally finite
・ Locally finite collection
Locally finite group
・ Locally finite measure
・ Locally finite operator
・ Locally finite poset
・ Locally finite space
・ Locally finite variety
・ Locally Hausdorff space
・ Locally integrable function
・ Locally listed buildings in Crawley
・ Locally nilpotent
・ Locally normal space
・ Locally profinite group
・ Locally regular space
・ Locally simply connected space
・ Locally testable code


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Locally finite group : ウィキペディア英語版
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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