Nihal YILMAZ, İ. Naci CANGÜL

5272

Conjugacy Classes of Elliptic Elements in the Picard Group

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.
Anahtar Kelimeler:

Turk. J. Math., 24, (2000), 209-220. Full text: pdf Other articles published in the same issue: Turk. J. Math., vol.24, iss.2.

Conjugacy Classes of Elliptic Elements in the Picard Group

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.
Keywords:

Turk. J. Math., 24, (2000), 209-220. Full text: pdf Other articles published in the same issue: Turk. J. Math., vol.24, iss.2.,

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Turkish Journal of Mathematics-Cover
  • ISSN: 1300-0098
  • Yayın Aralığı: 6
  • Yayıncı: TÜBİTAK
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