Fuchsian group


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Fuchsian group

[′fyük·sē·ən ‚grüp]
(mathematics)
A Kleinian group G for which there is a region D in the complex plane, consisting of either the interior of a circle or the portion of the plane on one side of a straight line, such that D is mapped onto itself by every element of G.
References in periodicals archive ?
Young researchers were exposed to the basic theory of the two in lectures on interval exchange maps and translation surfaces; unipotent flows and applications; quantitative nondivergence and its Diophantine applications; diagonal actions on locally homogenous spaces; and Fuchsian groups, geodesic flows on surfaces of constant negative curvature, and symbolic coding of geodesics.
Papers cover such subjects as outer automorphism groups of certain orientable Seifert three-manifold groups, a proposed public key cryptosystem using the modular group, normal subgroups of themodular group and other Hecke groups, unions of varieties and quasi-varieties, context-free irreducible word problems in groups, informative words and discreteness, using group theory for knowledge representation and discovery, torsion in maximal arithmetic Fuchsian groups, density of test elements in finite Abelian groups and the Rosenberg "monster.
Eleven chapters cover linear transformations, groups of linear transformations, Fuchsian groups, the Poincare theta series, the elementary groups, the elliptic modular functions, conformal mapping, uniformization and elementary and Fuchsian functions, uniformization and groups of Schottky type, and differential equations.