Free algebras of variety of unars with Malcev's operation $p$, define by identity $p(x,y,x)=y$

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.