What question did this study set out to answer?

The aim is to fully describe good involutions within free quandles and their subquandles, particularly in the context of twisted conjugation and Alexander quandles.

May 8, 2026Open Access

Good involutions of twisted conjugation subquandles and Alexander quandles

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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Authors

Lực Ta

Journals

Communications in Algebra

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University of Pittsburgh

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Good involutions of twisted conjugation subquandles and Alexander quandles

Key Points

Abstract

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Discussion

Authors

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References and Citations

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