Rank (Group)

For an arbitrary finitely generated Abelian Group $G$, the rank of $G$ is defined to be the rank of the Free generating Subset $G$ modulo its Torsion Subgroup. For a finitely generated Group, the rank is defined to be the rank of its ``Abelianization.''

See also Abelian Group, Betti Number, Burnside Problem, Quasithin Theorem, Quasi-Unipotent Group, Torsion (Group Theory)