A new proof for small cancellation conditions of 2-bridge link groups

TL;DR

This paper provides a simplified proof of small cancellation conditions for 2-bridge link groups and offers an alternative proof of a main result using transfinite induction, enhancing understanding of their algebraic structure.

Contribution

It introduces a new, simplified proof for small cancellation conditions and an alternative proof of a key result for 2-bridge link groups.

Findings

Simplified proof of small cancellation conditions

Alternative proof of the main result using transfinite induction

Enhanced understanding of 2-bridge link group presentations

Abstract

In this paper, we give a simple proof for the small cancellation conditions of the upper presentations of 2-bridge link groups, which holds the key to the proof of the main result of [1]. We also give an alternative proof of the main result of [1] using transfinite induction.