On the Cycle Structure of Finite Racks and Quandles

TL;DR

This paper investigates the cycle structure of automorphisms in finite racks and quandles, providing obstructions and verifying parts of a conjecture, thereby advancing understanding of their algebraic properties.

Contribution

It introduces new obstructions on cycle structures and verifies specific cases of Hayashi's conjecture for finite indecomposable racks and quandles.

Findings

Identified obstructions to cycle structures of inner automorphisms.

Verified some cases of Hayashi's conjecture.

Enhanced understanding of algebraic properties of racks and quandles.

Abstract

We provide obstructions on the cycle structure of inner automorphisms of finite indecomposable racks and quandles and verify some cases of a conjecture by C. Hayashi.