Solutions monomiales minimales irr\'eductibles dans $SL_{2}(\mathbb{Z}/p^{n}\mathbb{Z})$

Abstract

In this article, we study the combinatorics of congruence subgroups of the modular group. More precisely, we consider the notion of minimal monomial solutions. These are the solutions of a matrix equation (also appearing in the study of Coxeter friezes), modulo an integer $N$, whose components are identical and minimal for this property. The objective here is to characterize the solutions of this type verifying a property of irreducibility modulo a prime power.