Conjugacy classes of elliptic elements in the Picard group

Abstract

The Picard group P is a discrete subgroup of PSL(2, ℂ) with Gaussian integer coefficients. Here it is shown that the total number of conjugacy classes of elliptic elements of order 2 and 3 in P, which is given as seven by B. Fine [3], can actually be reduced to four and using this, the conditions for the maximal Fuchsian subgroups of P to have elliptic elements of orders 2 and 3 are found. © TÜBİTAK.