Every group is the group of self-homotopy equivalences of finite dimensional $\mathrm{CW}$-complex

We prove that any group $G$ occurs as $\mathcal{E}(X)$, where $X$ is a $\mathrm{CW}$-complex of finite dimension and $\mathcal{E}(X)$ denotes its group of self-homotopy equivalences. Thus, we generalize a well-known theorem due to Costoya and Viruel [9] asserting that any finite group occurs as $\mathcal{E}(X)$, where $X$ is rational elliptic space.
Bibliography: 12 titles.