The ratio and generating function of cogrowth coefficients of finitely generated groups

• Autorzy: Ryszard Szwarc
• Języki publikacji: EN

Abstrakty

EN

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 $γ_n$.

Słowa kluczowe

EN

cogrowth of subgroups; free group; amenable groups

Kategorie tematyczne

• 20E05: Free nonabelian groups
• 20F05: Generators, relations, and presentations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1998
• Tom: 131
• Numer: 1
• Strony: 89-94

Daty

wydano

1998

otrzymano

1997-11-03

Twórcy

autor

Ryszard Szwarc

• Institute of Mathematics, Wrocław University, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Bibliografia

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