Editing Local property (section)

==Properties of infinite groups==
For an [[infinite group]], a "small neighborhood" is taken to be a [[finitely generated group|finitely generated]] [[subgroup]].  An infinite group is said to be '''locally ''P''''' if every finitely generated subgroup is ''P''.  For instance, a group is [[locally finite group|locally finite]] if every finitely generated subgroup is finite, and a group is locally soluble if every finitely generated subgroup is [[soluble group|soluble]].