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...tion is the ''only'' infinite cyclic group, in the sense that any infinite cyclic group is [[group isomorphism|isomorphic]] to '''Z'''.

...l)|vectors]] in the plane, and the various [[finite groups]] such as the [[cyclic group]]s that are the group of integers [[modular arithmetic|modulo]] ''n''. [[Se

...bra]] of the [[monoid]] of non-negative powers of the generator ''X'' of a cyclic group. This method also allows one to define non-commuting polynomial rings, and