Abstract
In this work, we find a system of generators for the Picard modular group \(SU(2,1,{\mathcal {O}}_{11})\). This system contains four transformations, two translations a rotation and an involution.
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References
Falbel E, Francsics G, Lax PD, Parker JR (2011) Generators of a Picard modular group in two complex dimensions. Proc Am Math Soc 139:2439–2447
Falbel E, Francsics G, Parker JR (2011) The geometry of the Gauss–Picard modular group. Math Ann 349:459–508
Falbel E, Parker JR (2006) The geometry of the Eisenstein–Picard modular group. Duke Math J 131:249–289
Goldman WM (1999) Complex hyperbolic geometry. Oxford University Press, Oxford
Hardy GH, Wright EM (1954) An introduction to the theory of numbers. Oxford University Press, Oxford
Parker JR (2003) Notes on complex hyperbolic geometry. Preliminary version
Stewart IN, Tall DO (1979) Algebraic number theory. Chapman and Hall Ltd., London
Wang J, Xiao Y, Xie B (2011) Generators of the Eisenstein–Picard modular groups. J Aust Math Soc 91:421–429
Zhao T (2012) Generators for the Euclidean Picard modular groups. Trans Am Math Soc 364:3241–3263
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Ghoshouni, M., Heydarpour, M. A Generating Set for the Picard Modular Group in the Case \(d=11\). Iran J Sci Technol Trans Sci 44, 1469–1475 (2020). https://doi.org/10.1007/s40995-020-00970-9
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DOI: https://doi.org/10.1007/s40995-020-00970-9