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Group theory with functions

Source: Miklos Schweitzer 2023, Problem 5

March 7, 2024
group theoryfunctionabstract algebra

Problem Statement

Let GG{} be an arbitrary finite group, and let tn(G)t_n(G) be the number of functions of the form f:G^n\to G,  f(x_1,x_2,\ldots,x_n)=a_0x_1a_1\cdots x_na_n (a_0,\ldots,a_n\in G).Determine the limit of tn(G)1/nt_n(G)^{1/n} as nn{} tends to infinity.
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