Good involutions of twisted conjugation subquandles and Alexander quandles
Luc Ta
TL;DR
This paper classifies and enumerates good involutions in various classes of quandles, including Alexander and linear quandles, providing explicit mappings and characterizations.
Contribution
It offers a complete description of good involutions in free, sub, and Alexander quandles, and characterizes connected, involutory Alexander quandles.
Findings
Complete description of good involutions in free and subquandles of twisted conjugation quandles.
Enumeration of good involutions of linear quandles up to order 23.
Characterization of connected, involutory Alexander quandles.
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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