Conjugacy Classes of Elliptic Elements in the Picard Group

Authors

NİHAL YILMAZ
İSMAİL NACİ CANGÜL

DOI

-

Abstract

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

First Page

209

Last Page

220

Recommended Citation

YILMAZ, NİHAL and CANGÜL, İSMAİL NACİ (2000) "Conjugacy Classes of Elliptic Elements in the Picard Group," Turkish Journal of Mathematics: Vol. 24: No. 2, Article 8. Available at: https://journals.tubitak.gov.tr/math/vol24/iss2/8