3 Addendum to “ Groups of Ribbon Knots ”

The purpose of this document is to clarify the inductive step described in the proof of Theorem 3.2 in [2]. In the second last sentence of the proof, it says, ‘it follows from the inductive proof that Rn is of index two.’ The question of how this assertion is verified was first raised by Dror Bar Natan and his student Ofer Ron [1]. To avoid any confusions that may arise in the future, the author of the paper [2] would like to fill in the details to show that Rn is of index two. Readers of this document are assumed to have familiarity with [2]. For your reference, Theorem 3.2 is stated below.