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Locally cyclic group

Revision as of 00:15, 6 January 2009 by Vipul (talk | contribs) (New page: {{group property}} ==Definition== A group is termed '''locally cyclic''' if it satisfies the following equivalent conditions: # Every finitely generated...)
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Definition

A group is termed locally cyclic if it satisfies the following equivalent conditions:

  1. Every finitely generated subgroup of the group is cyclic.
  2. The subgroup generated by any two elements of the group is cyclic.
  3. Its lattice of subgroups is a distributive lattice. In other words, the operations of join of subgroups and intersection of subgroups distribute over each other.

Relation with other properties