The ratio and generating function of cogrowth coefficients of finitely generated groups
| dc.creator | Szwarc, Ryszard | |
| dc.date | 2007-11-22 | |
| dc.date.accessioned | 2026-07-07T08:44:31Z | |
| dc.date.available | 2026-07-07T08:44:31Z | |
| dc.description | Let G be a group generated by $r$ elements $g_1,g_2,..., g_r.$ Among the reduced words in $g_1,g_2,..., g_r$ of length $n$ some, say $γ_n,$ represent the identity element of the group $G.$ It has been shown in a combinatorial way that the $2n$th root of $γ_{2n}$ has a limit, called the cogrowth exponent with respect to generators $g_1,g_2,..., g_r.$ We show by analytic methods that the numbers $γ_n$ vary regularly; i.e. the ratio $γ_{2n+2}/γ_{2n}$ is also convergent. Moreover we derive new precise information on the domain of holomorphy of $γ(z),$ the generating function associated with the coefficients $γ_n.$ | |
| dc.identifier | https://arxiv.org/abs/0711.3514 | |
| dc.identifier | http://arxiv.org/abs/0711.3514 | |
| dc.identifier | Studia Mathematica 131 (1998), 89-94 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/142682 | |
| dc.subject | Functional Analysis | |
| dc.subject | Group Theory | |
| dc.subject | 20F05; 20E05 | |
| dc.title | The ratio and generating function of cogrowth coefficients of finitely generated groups | |
| dc.type | text |