A Generating Set for the Picard Modular Group in the Case $$d=11$$

Ghoshouni, Mahboubeh; Heydarpour, Majid

doi:10.1007/s40995-020-00970-9

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2021

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“…This is done in section 7. Note that the methods used in this paper should work for all 1-cusped Picard groups (this happens for slightly more values of d, namely d = 1, 2, 3,7,11,19,43,67,163), but they would require much heavier computation (presentations are known only for d = 1, 2, 3, 7, 11, see [4], [3], [8], [11], [6], [5]).…”

Section: Introductionmentioning

confidence: 99%

On the geometry of a Picard modular group

Deraux¹

2021

Preprint

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We study geometric properties of the action of the Picard modular group Γ = P U (2, 1, O 7 ) on the complex hyperbolic plane H 2 C , where O 7 denotes the ring of algebraic integers in Q(i √ 7). We list conjugacy classes of maximal finite subgroups in Γ, we give an explicit description of the Fuchsian subgroups that occur as stabilizers of mirrors of complex reflections in Γ. As an application, we show the existence of a torsion-free subgroup of index 336 in Γ.

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Section: Introductionmentioning

confidence: 99%

On the geometry of a Picard modular group

Deraux¹

2021

Preprint

View full text Add to dashboard Cite

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A Generating Set for the Picard Modular Group in the Case $$d=11$$

Cited by 1 publication

References 7 publications

On the geometry of a Picard modular group

On the geometry of a Picard modular group

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