| Título: | The aspherical Cavicchioli–Hegenbarth–Repovš generalized Fibonacci groups |
| Autores: | Williams, Gerald |
| Fecha: | 2009 |
| Publicador: | De Gruyter |
| Fuente: |
Ver documento |
| Tipo: |
Article PeerReviewed |
| Tema: | QA Mathematics |
| Descripción: | The Cavicchioli-Hegenbarth-Repovš generalized Fibonacci groups are defined by the presentations Gn(m; k) = h x1; : : : ; xn j xixi+m = xi+k (1 · i · n) i. These cyclically presented groups generalize Conway's Fibonacci groups and the Sieradski groups. Building on a theorem of Bardakov and Vesnin we classify the aspherical presentations Gn(m; k). We determine when Gn(m; k) has in¯nite abelianization and provide su±cient conditions for Gn(m; k) to be perfect. We conjecture that these are also necessary conditions. Combined with our asphericity theorem, a proof of this conjecture would imply a classification of the finite Cavicchioli-Hegenbarth-Repovš groups. |
| Idioma: | No aplica |