2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/212318We give an easy proof of Schützenberger's Theorem stating that non-commutative formal power series are rational if and only if they are recognisable. A byproduct of this proof is a natural metric on a subgroup of invertible rational non-commutative power series. We describe a few features of this metric group.41 pagesCombinatoricsGroup TheoryThe special subgroup of invertible non-commutative rational power series as a metric grouptext