# Degree of satisfiability of some special equations

@article{Kocsis2020DegreeOS, title={Degree of satisfiability of some special equations}, author={Zoltan A. Kocsis}, journal={arXiv: Group Theory}, year={2020} }

A well-known theorem of Gustafson states that in a non-Abelian group the degree of satisfiability of $xy=yx$, i.e. the probability that two uniformly randomly chosen group elements $x,y$ obey the equation $xy=yx$, is no larger than $\frac{5}{8}$. The seminal work of Antolin, Martino and Ventura (arXiv:1511.07269) on generalizing the degree of satisfiability to finitely generated groups led to renewed interest in Gustafson-style properties of other equations. Positive results have recently been… CONTINUE READING

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