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First we give simple examples of abelian $p$-group $G$ and non-abelian $p$-group $G'$ of order $p^m, \\; m \\geq 3$ for odd $p$ (resp. $2^m, \\; m \\geq 4$) for which $\\zeta_G(s) = \\zeta_{G'}(s)$. Hence we see there are many non-abelian groups whose zeta functions have symmetry and Euler product, like the case of abelian groups. 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