Virtually cyclic group
= Virtually cyclic group
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A group is virtually cyclic when it has a cyclic <subgroup> of finite index. A finitely generated <abelian group> is virtually cyclic exactly when its free abelian rank is at most one. Finite <groups> qualify because their trivial <cyclic subgroup> has finite <subgroup index>. The rank-one case is the infinite finitely generated <abelian group> case.