On a conjecture about profiles of finite connected racks
Group Theory
2021-09-30 v3 Combinatorics
Abstract
A rack is a set with a binary operation such that left multiplications are automorphisms of the set and a quandle is a rack satisfying a certain condition. For a finite connected rack the cycle type of the permutation defined by left multiplication by an element is independent from the chosen element. This cycle type is called the profile of the rack. Hayashi conjectured, in the profile of a finite connected quandle, the length of a cycle must divide the length of the largest cycle. In this paper, we prove Hayashi's Conjecture in some particular cases.
Cite
@article{arxiv.2006.10327,
title = {On a conjecture about profiles of finite connected racks},
author = {Selçuk Kayacan},
journal= {arXiv preprint arXiv:2006.10327},
year = {2021}
}