Distinguishing some genus one knots using finite quotients

Abstract

We give a criterion for distinguishing a prime knot [Formula: see text] in [Formula: see text] from every other knot in [Formula: see text] using the finite quotients of [Formula: see text]. Using recent work of Baldwin–Sivek, we apply this criterion to the hyperbolic knots [Formula: see text], [Formula: see text], and the three-strand pretzel knots [Formula: see text] for every integer [Formula: see text].