Algebraic entropy of generalized shifts on direct products

For a set $\mathrm{\Gamma }$, a function $\lambda :\mathrm{\Gamma }\to \mathrm{\Gamma }$ and a non-trivial abelian group $K$, the generalized shift ${\sigma }_{\lambda }:K^{\mathrm{\Gamma }}\to K^{\mathrm{\Gamma }}$ is defined by $(x_i{)}_{i\in \mathrm{\Gamma }}\mapsto (x_{\lambda (i)}{)}_{i\in \mathrm{\Gamma }}$. In this paper we compute the algebraic entropy of ${\sigma }_{\lambda }$; it is either zero or infinite, depending exclusively on the properties of $\lambda$.