On conjugacy classes of congruence subgroups of PSL(2,R)
C. J. Cummins
Abstract: Let 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.
|
