Growth rates of amenable groups
| dc.creator | Arzhantseva, Goulnara | |
| dc.creator | Guba, Victor | |
| dc.creator | Guyot, Luc | |
| dc.date | 2004-06-01 | |
| dc.date | 2004-06-15 | |
| dc.date.accessioned | 2026-07-07T05:08:46Z | |
| dc.date.available | 2026-07-07T05:08:46Z | |
| dc.description | Let $F_m$ be a free group with $m$ generators and let $R$ be its normal subgroup such that $F_m/R$ projects onto $\zz$. We give a lower bound for the growth rate of the group $F_m/R'$ (where $R'$ is the derived subgroup of $R$) in terms of the length $ρ=ρ(R)$ of the shortest nontrivial relation in $R$. It follows that the growth rate of $F_m/R'$ approaches $2m-1$ as $ρ$ approaches infinity. This implies that the growth rate of an $m$-generated amenable group can be arbitrarily close to the maximum value $2m-1$. This answers an open question by P. de la Harpe. In fact we prove that such groups can be found already in the class of abelian-by-nilpotent groups as well as in the class of finite extensions of metabelian groups. | |
| dc.description | 6 pages | |
| dc.identifier | https://arxiv.org/abs/math/0406013 | |
| dc.identifier | http://arxiv.org/abs/math/0406013 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71398 | |
| dc.subject | Group Theory | |
| dc.subject | 20F65; 05C25 | |
| dc.title | Growth rates of amenable groups | |
| dc.type | text |