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[TMJ] The Modular Group

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New THE MATHEMATICA JOURNAL article:


The Modular Group: A Finitely Generated Group with Interesting Subgroups

by PAUL R. MCCREARY, TERI JO MURPHY, CHRISTAN CARTER


ABSTRACT: 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 enter image description here and an element of infinite order enter image description here. 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.

enter image description here

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