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Suppose S a finite set of generators for a group G. As in Sect. 2.1 , \(l:G\to {\mathbb N}\) is word length. Define a power series \(f(t)\) (the growth series of G) by \(f(t):=\sum _{g\in G} t^{l(g)}\) .

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Growth Series

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  • 发表日期：

    2025年

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  • Michael W. Davis

摘要

Suppose S a finite set of generators for a group G. As in Sect. 2.1 , \(l:G\to {\mathbb N}\) is word length. Define a power series \(f(t)\) (the growth series of G) by \(f(t):=\sum _{g\in G} t^{l(g)}\) .