k-Free-like groups

• Autores: Alexander Yu. Olshanskii, Mark V. Sapir
• Localización: Algebra and logic, ISSN 0002-5232, Vol. 48, Nº. 2, 2009, págs. 140-146
• Idioma: inglés
• DOI: 10.1007/s10469-009-9044-2
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• Resumen

  • The following results are proved. In Theorem 1, it is stated that there exist both finitely presented and not finitely presented 2-generated nonfree groups which are k-free-like for any k ? 2. In Theorem 2, it is claimed that every nonvirtually cyclic (resp., noncyclic and torsion-free) hyperbolic m-generated group is k-free-like for every k ? m + 1 (resp., k ? m). Finally, Theorem 3 asserts that there exists a 2-generated periodic group G which is k-free-like for every k ? 3.