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Hayashi Property for Conjugation Quandles

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arxiv 2503.22377 v1 pith:ELNS3L64 submitted 2025-03-28 math.GR

Filip Filipi This is my paper · ORCID
classification math.GR
keywords conditionconjectureconjugationhayashiquandlesfinitegroupsalternating
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We give a comprehensive description of conjugation quandles and their connectedness. In this context, we find a characterization of Hayashi's conjecture (2013) in terms of a centrality condition of groups. This condition is thus a conjecture itself and it states that powers of elements of a finite and generating conjugacy classes should be central whenever they commute with one particular element of this class. We prove this condition in several cases, e.g. for finite nilpotent, symmetric, alternating, and dihedral groups. All of these results translate to Hayashi's conjecture for the corresponding conjugation quandles.

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  1. Good involutions of conjugation subquandles

    math.GT 2025-05 accept novelty 7.0 of 10

    Good involutions of conjugation subquandles and core quandles are characterized by central-valued functions, with algorithms, enumeration data, new CNS-quandle families, and a category equivalence between racks and Le...

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