Abstract

PUMMERENKE, CHRISTIAN  and  TORO, MARGARITA. On a family of groups generated by parabolic matrices. Rev.colomb.mat. [online]. 2019, vol.53, n.2, pp.221-236.  Epub Mar 20, 2020. ISSN 0034-7426.

We study various aspects of the family of groups generated by the parabolic matrices A(t 1 ζ),. .. , A(t m ζ) where A(z) = () and by the elliptic matrix (). The elements of the matrices W in such groups can be computed by a recursion formula. These groups are special cases of the generalized parametrized modular groups introduced in [16].

We study the sets {z : tr W(z) Є [-2, +2]} [13] and their critical points and geometry, furthermore some finite index subgroups and the discretness of subgroups.

Keywords : modular group; parametrized modular group; singular set; discrete groups; Chebyshev polynomials.

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