  Given a map $f\colon X \to Y$, we extend a Gottlieb's result to the
generalized Gottlieb group $G^f(Y,f(x_0))$ and show that the canonical
isomorphism $\pi_1(Y,f(x_0))\xrightarrow{\approx}\mathcal{D}(Y)$ restricts to
an isomorphism
$G^f(Y,f(x_0))\xrightarrow{\approx}\mathcal{D}^{\tilde{f}_0}(Y)$, where
$\mathcal{D}^{\tilde{f}_0}(Y)$ is some subset of the group $\mathcal{D}(Y)$ of
deck transformations of $Y$ for a fixed lifting $\tilde{f}_0$ of $f$ with
respect to universal coverings of $X$ and $Y$, respectively.
