Abstract
AbstractLet G be a subgroup of PSL(2, R) which is commensurable with PSL(2, Z). We say that G is a congruence subgroup of PSL(2, R) if G contains a principal congruence subgroup /overline Γ(N) for some N. An algorithm is given for determining whether two congruence subgroups are conjugate in PSL(2, R). This algorithm is used to determine the PSL(2, R) conjugacy classes of congruence subgroups of genus-zero and genus-one. The results are given in a table.
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