Verbal quandles with one parameter
E. Markhinina, T. Nasybullov

TL;DR
This paper characterizes all words in three variables that define verbal quandles with one parameter, ensuring the algebraic system forms a quandle in any group and element.
Contribution
It provides a complete classification of words in the free group that generate verbal quandles with one parameter.
Findings
Identifies all words W(x,y,z) that produce quandles in any group G with element c.
Establishes conditions under which the algebraic system (G,*_{W,c}) is a quandle.
Contributes to the understanding of verbal constructions in quandle theory.
Abstract
We find all words in the free group , such that for every group and an element the algebraic system with the binary operation given by for is a quandle. Such quandles are called verbal quandles with one parameter.
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Taxonomy
Topicssemigroups and automata theory · Geometric and Algebraic Topology · Finite Group Theory Research
