The Modular Group A Finitely Generated Group with Interesting Subgroups
نویسندگان
چکیده
The action of Möbius transformations with real coefficients preserves the hyperbolic metric in the upper half-plane model of the hyperbolic plane. The modular group is an interesting group of hyperbolic isometries generated by two Möbius transformations, namely, an order-two element, g2 HzL = -1 ê z, and an element of infinite order, g• HzL = z + 1. Viewing the action of the group elements on a model of the hyperbolic plane provides insight into the structure of hyperbolic 2-space. Animations provide dynamic illustrations of this action.
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