On a Conjecture about Profiles of Finite Connected Racks

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Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi
Cilt: 18 Sayı: 3
On a Conjecture about Profiles of Finite Connected Racks

On a Conjecture about Profiles of Finite Connected Racks

Authors : Selçuk Kayacan

Pages : 735-744

View : 45 | Download : 85

Publication Date : 2025-12-31

Article Type : Research Paper

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.
Keywords : Sonlu bağlantılı rak, rakın profili, Hayashi’nin sanısı

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