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}
}
  • Irina Gelbukh
  • Published 2015
  • Mathematics
  • Czechoslovak Mathematical Journal
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
5 Citations

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