# [TMJ] The Modular Group

Posted 2 years ago
1409 Views
|
0 Replies
|
0 Total Likes
|

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 and an element of infinite order . 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.