# Co-rank and Betti number of a group

@article{Gelbukh2015CorankAB, title={Co-rank and Betti number of a group}, author={Irina Gelbukh}, journal={Czechoslovak Mathematical Journal}, year={2015}, volume={65}, pages={565-567} }

For a finitely generated group, we study the relations between its rank, the maximal rank of its free quotient, called co-rank (inner rank, cut number), and the maximal rank of its free abelian quotient, called the Betti number. We show that any combination of the group’s rank, co-rank, and Betti number within obvious constraints is realized for some finitely presented group (for Betti number equal to rank, the group can be chosen torsion-free). In addition, we show that the Betti number is… Expand

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