On killers of cable knots groups

TL;DR

This paper investigates the properties of cable knot groups, demonstrating that they contain infinitely many elements that generate the group normally, with each element belonging to a distinct automorphic orbit.

Contribution

It proves the existence of infinitely many killers in cable knot groups, each in a different automorphic orbit, highlighting a rich structure of these groups.

Findings

Cable knot groups have infinitely many killers.

No two killers are related by automorphisms.

The structure of killers reflects the complexity of cable knot groups.

Abstract

A killer of a group Gis an element that normally generates G. We show that the group of a cable knot contains infinitely many killers such that no two lie in the same automorphic orbit.