References of "Juriaans, S. O."
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See detailDirichlet-Ford domains and double Dirichlet domains
Jespers, E.; Juriaans, S. O.; Kiefer, Ann UL et al

in Bulletin of the Belgian Mathematical Society Simon Stevin (2016), 23(3), 465--479

We continue investigations started by Lakeland on Fuchsian and Kleinian groups which have a Dirichlet fundamental domain that also is a Ford domain in the upper half-space model of hyperbolic 2- and 3 ... [more ▼]

We continue investigations started by Lakeland on Fuchsian and Kleinian groups which have a Dirichlet fundamental domain that also is a Ford domain in the upper half-space model of hyperbolic 2- and 3-space, or which have a Dirichlet domain with multiple centers. Such domains are called DF-domains and Double Dirichlet domains respectively. Making use of earlier obtained concrete formulas for the bisectors defining the Dirichlet domain of center i ∈ H 2 or center j ∈ H 3 , we obtain a simple condition on the matrix entries of the side- pairing transformations of the fundamental domain of a Fuchsian or Kleinian group to be a DF-domain. Using the same methods, we also complement a result of Lakeland stating that a cofinite Fuchsian group has a DF domain (or a Dirichlet domain with multiple centers) if and only if it is an index 2 subgroup of the discrete group G of reflections in a hyperbolic polygon. [less ▲]

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See detailFrom the Poincaré theorem to generators of the unit group of integral group rings of finite groups
Jespers, E.; Juriaans, S. O.; Kiefer, Ann UL et al

in Mathematics of Computation (2015), 84(293), 1489--1520

We give an algorithm to determine finitely many generators for a subgroup of finite index in the unit group of an integral group ring ZG of a finite nilpotent group G, this provided the rational group ... [more ▼]

We give an algorithm to determine finitely many generators for a subgroup of finite index in the unit group of an integral group ring ZG of a finite nilpotent group G, this provided the rational group algebra QG does not have simple components that are division classical quaternion algebras or two-by-two matrices over a classical quaternion algebra with centre Q. The main difficulty is to deal with orders in quaternion algebras over the rationals or a quadratic imaginary extension of the rationals. In order to deal with these we give a finite and easy implementable algorithm to compute a fundamental domain in the hyperbolic three space H 3 (respectively hyperbolic two space H 2 ) for a discrete subgroup of PSL 2 (C) (respectively PSL 2 (R)) of finite covolume. Our results on group rings are a continuation of earlier work of Ritter and Sehgal, Jespers and Leal. [less ▲]

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