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Does there exist Fuchsian groups, which canis not be conjugated insidein$SL(2, \mathbb{R})$ to a subgroup of $SL(2, \mathbb{Z})$, but containstill contains a congruence subgroup?
Does there exist Fuchsian groups, which can not be conjugated inside$SL(2, \mathbb{Z})$ but contain a congruence subgroup?
Does there exist Fuchsian groups, which is not conjugated in$SL(2, \mathbb{R})$ to a subgroup of $SL(2, \mathbb{Z})$, but still contains a congruence subgroup?
