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Let Aut$_∗(X)$ denote the group of homotopy classes of self-homotopy equivalences of $X$, which induce identity automorphisms of homology group. We describe a decomposition of Aut$_∗(X_1∨· · ·∨X_n)$ as a product of its simpler subgroups. We consider the subgroup Aut$_Σ(X)$ of all self homotopy classes α of $X$ such that $Σα = 1_{ΣX} : ΣX → ΣX$, and also give some properties of Aut$_Σ(X)$.
}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19291.html} }Let Aut$_∗(X)$ denote the group of homotopy classes of self-homotopy equivalences of $X$, which induce identity automorphisms of homology group. We describe a decomposition of Aut$_∗(X_1∨· · ·∨X_n)$ as a product of its simpler subgroups. We consider the subgroup Aut$_Σ(X)$ of all self homotopy classes α of $X$ such that $Σα = 1_{ΣX} : ΣX → ΣX$, and also give some properties of Aut$_Σ(X)$.