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.
Categories: math.AT