Geodesic
Free algebras of variety of unars with Malcev's operation $p$, define by identity $p(x,y,x)=y$
Čebyševskij sbornik, Tome 12 (2011) no. 2, pp. 127-134

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In article is given construction of free algebras of the variety of algebras with one unary and one ternary Mal'cev's operation $p$, provided that operations is commute, defined by identity $p(x,y,x)=y$. It is proved decidability of word problem in free algebras and uniqueness of free basis. It is proved realization of Hopf property for free algebras of finitely rank. 
@article{CHEB_2011_12_2_a15,
     author = {V. L. Usol'cev},
     title = {Free algebras of variety of unars with {Malcev's} operation $p$, define by identity $p(x,y,x)=y$},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {127--134},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2011_12_2_a15/}
}
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V. L. Usol'cev. Free algebras of variety of unars with Malcev's operation $p$, define by identity $p(x,y,x)=y$. Čebyševskij sbornik, Tome 12 (2011) no. 2, pp. 127-134. http://geodesic.mathdoc.fr/item/CHEB_2011_12_2_a15/