Solving the membership problem for certain subgroups of $SL_2(\mathbb{Z})$

Author name not available (Why is that?)

Publication date: 5 October 2021

Abstract: For positive integers

u

and

v

, let

and

. Let

G_{u, v}

be the group generated by

L_{u}

and

R_{v}

. In a previous paper, the authors determined a characterization of matrices

in

G_{u, v}

when

u, v g e q 3

in terms of the short continued fraction representation of

b / d

. We extend this result to the case where

u + v > 4

. Additionally, we compute

[m a t h s c r G_{u, v} c o l o n G_{u, v}]

for

u, v g e q 1

, extending a result of Chorna, Geller, and Shpilrain.

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