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Elementary amenable groups: the smallest class of groups which includes finite groups and commutative groups, and is closed under formation of subgroupshomomorphic images, factor groupssubgroups, group extensions (by an other element of the class) and direct limitsdirected unions. (See http://en.wikipedia.org/wiki/Elementary_amenable_group)

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Elementary groups: the smallest class of groups which includes finite groups and commutative groups, and is closed under formation of subgroups, factor groups, group extensions (by an other element of the class) and direct limits.

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Elementary groups: the smallest class of groups which includes finite groups and commutative groups, and is closed under formation of subgroups, factor groups, and direct limits.