• Honam Mathematical Journal
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• v.44 no.2
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• pp.296-309
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• 2022

In this paper, we establish the Fricke Group Γ_F (N) which is a new special group of Non-Euclidean Crystallograhic (NEC) group. We obtain this group whose congruence subgroup Γ₀(N) is expanded with Fricke reflection $F(z)={\frac{1}{N{\bar{z}}}}$. Then, we research and calculate the structure of signature and fundamental domain of this group. And then, we calculate the number of boundary components in the signature for this group. Finally, we find the 2, 3, ∞ valued link periods of these boundary components with the H. Jaffee technique.