Deficiency and abelianized deficiency of some virtually free groups

• Autores: Martin R. Bridson, Michael Tweedale
• Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 143, Nº 2, 2007, págs. 257-264
• Idioma: inglés
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• Resumen

  • Let Qm be the HNN extension of Z/m × Z/m where the stable letter conjugates the first factor to the second. We explore small presentations of the groups Gm,n = Qm* Qn. We show that for certain choices of (m,n), for example (2,3), the group Gm,n has a relation gap unless it admits a presentation with at most 3 defining relations, and we establish restrictions on the possible form of such a presentation. We then associate to each (m,n) a 3-complex with 16 cells. This 3-complex is a counterexample to the D(2) conjecture if Gm,n has a relation gap.