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May 8, 2026Communications in Algebra0 citationsOpen Access

Good involutions of twisted conjugation subquandles and Alexander quandles

LTLực Ta

Key Points

  • The aim is to fully describe good involutions within free quandles and their subquandles, particularly in the context of twisted conjugation and Alexander quandles.
  • Characterization of good involutions of free and twisted conjugation quandles.
  • Enumeration of good involutions for linear quandles up to order 23 using computer search.
  • Explicit mappings provided for identified involutions.
  • All good involutions of Alexander quandles are completely characterized.
  • Enumeration results for linear quandles show distinct involutions up to order 23.
  • Connected, involutory Alexander quandles are fully characterized, revealing potential independent interest.

Abstract

We completely describe good involutions of free quandles and subquandles of twisted conjugation quandles of groups, including all Alexander quandles. As an application, we enumerate good involutions of linear quandles, and we provide explicit mappings for those up to order 23 via a computer search. Along the way, we completely characterize connected, involutory Alexander quandles, which may be of independent interest.

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Cite This Study

Lực Ta (2026) studied this question.

synapsesocial.com/papers/69fd7d4abfa21ec5bbf05ca4https://doi.org/10.1080/00927872.2026.2643415
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1Classification of generalized Alexander quandles2024
  2. 2Structure groups and second homology groups of linear Alexander quandles2025
  3. 3Alexander Matrices of Link Quandles Associated to Quandle Homomorphisms and Quandle Cocycle Invariants2024
  4. 4Multivariate Alexander quandles, VI. Metabelian groups and 2-component links2024
  5. 5Computing the associated groups of quandles with tools from group homology theory2024