- Tytuł:
- The ratio and generating function of cogrowth coefficients of finitely generated groups
- Autorzy:
- Szwarc, Ryszard
- Powiązania:
- https://bibliotekanauki.pl/articles/1217941.pdf
- Data publikacji:
- 1998
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
cogrowth of subgroups
free group
amenable groups - Opis:
- Let G be a group generated by r elements $g_1,…,g_r$. Among the reduced words in $g_1,…,g_r$ 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 2nth root of $γ_{2n}$ has a limit, called the cogrowth exponent with respect to the generators $g_1,…,g_r$. 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 $γ_n$.
- Źródło:
-
Studia Mathematica; 1998, 131, 1; 89-94
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł