THE KNOT QUANDLES OF SUCIU’S RIBBON <i>n</i> -KNOTS AND AUTOMORPHISMS ON THE FREE GROUP OF RANK TWO

Abstract Jabłonowski [‘On biquandle-based invariant of immersed surface-links, Yoshikawa oriented fifth move, and ribbon 2-knots’, Preprint, 2025, arXiv:2505.14724] proved that the knot quandles of Suciu’s n -knots, which share isomorphic knot groups, are mutually nonisomorphic, and Yasuda [‘Knot quandles distinguish Suciu’s ribbon knots’, Preprint, 2025, arXiv:2508.15129] later gave a different proof. We present yet another proof of this result by analysing the conjugacy classes of certain automorphisms of the free group of rank two.