A note on models of identities (Q1112856)

In Ann. Inst. Mat., Univ. Nac. Auton. Mex. 20, 127-156 (1980; Zbl 0501.08003), as the simplest example of identities having a rather surprising property of possessing infinite models but no nontrivial finite models, \textit{W. Taylor} points out Austin's identity: \(((y^ 2\cdot y)x)((y^ 2\cdot (y^ 2\cdot y))z)=x\) [\textit{A. K. Austin}, Proc. Am. Math. Soc. 16, 522-523 (1965; Zbl 0137.008)] and the system of three simple identities: \(x'x^*=x\), \((xy)'=x\), \((xy)^*=y\), where ' and \({}^*\) stand for unary operators. In this connection, we present the following Theorem: Each nontrivial model of the identity \((x'y)z=y\) is infinite.