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

2020 ◽  
Vol 44 (5) ◽  
pp. 1469-1475
Author(s):  
Mahboubeh Ghoshouni ◽  
Majid Heydarpour
Keyword(s):  
Modular Group ◽  
Generating Set ◽  
Picard Modular Group

scholarly journals GENERATORS OF THE EISENSTEIN–PICARD MODULAR GROUP

2011 ◽  
Vol 91 (3) ◽  
pp. 421-429 ◽  
Author(s):  
JIEYAN WANG ◽  
YINGQING XIAO ◽  
BAOHUA XIE
Keyword(s):  
Modular Group ◽  
Picard Modular Group

AbstractWe prove that the Eisenstein–Picard modular group SU(2,1;ℤ[ω3]) can be generated by four given transformations.

scholarly journals Generators for Alternating and Symmetric Groups

1971 ◽  
Vol 12 (1) ◽  
pp. 63-68 ◽  
Author(s):  
I. M. S. Dey ◽  
James Wiegold
Keyword(s):  
Free Product ◽  
Modular Group ◽  
Symmetric Groups ◽  
Alternating Groups ◽  
Generating Set ◽  
Alternating And Symmetric Groups

Let Γ denote the modular group, that is, the free product of a group of order 2 and a group of order 3. Morris Newman investigates in [2] the factor-groups of Γ and calls them Γ-groups for short; thus a group is a Γ-group if and only if it has a generating set consisting of an element of order dividing 2 and an element of order dividing 3. Newman's interest centres on finite simple Γ-groups. He proves that the linear fractional groups LF(2,p) for primes p are Γ -groups, and poses the problem of deciding which of the alternating groups enjoy this property.

scholarly journals Analysis of a Picard modular group

2006 ◽  
Vol 103 (30) ◽  
pp. 11103-11105 ◽  
Author(s):  
G. Francsics ◽  
P. D. Lax
Keyword(s):  
Modular Group ◽  
Picard Modular Group

scholarly journals Generators of a Picard modular group in two complex dimensions

2010 ◽  
Vol 139 (7) ◽  
pp. 2439-2447 ◽  
Author(s):  
Elisha Falbel ◽  
Gábor Francsics ◽  
Peter D. Lax ◽  
John R. Parker
Keyword(s):  
Modular Group ◽  
Complex Dimensions ◽  
Picard Modular Group

The geometry of the Gauss–Picard modular group

2010 ◽  
Vol 349 (2) ◽  
pp. 459-508 ◽  
Author(s):  
Elisha Falbel ◽  
Gábor Francsics ◽  
John R. Parker
Keyword(s):  
Modular Group ◽  
Picard Modular Group

scholarly journals Generators of the Gauss–Picard modular group in three complex dimensions

2015 ◽  
Vol 273 (1) ◽  
pp. 197-211 ◽  
Author(s):  
BaoHua Xie ◽  
JieYan Wang ◽  
YuePing Jiang
Keyword(s):  
Modular Group ◽  
Complex Dimensions ◽  
Picard Modular Group

A minimal volume arithmetic cusped complex hyperbolic orbifold

2010 ◽  
Vol 150 (2) ◽  
pp. 313-342 ◽  
Author(s):  
TIEHONG ZHAO
Keyword(s):  
Fundamental Domain ◽  
Modular Group ◽  
Minimal Volume ◽  
Hyperbolic Orbifold ◽  
Group A ◽  
Picard Modular Group

AbstractThe sister of Eisenstein–Picard modular group is described explicitly in [10], whose quotient is a noncompact arithmetic complex hyperbolic 2-orbifold of minimal volume (see [16]). We give a construction of a fundamental domain for this group. A presentation of that lattice can be obtained from that construction, which relates to one of Mostow's lattices.

scholarly journals The geometry of the Eisenstein-Picard modular group

2006 ◽  
Vol 131 (2) ◽  
pp. 249-289 ◽  
Author(s):  
Elisha Falbel ◽  
John R. Parker
Keyword(s):  
Modular Group ◽  
Picard Modular Group
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