(untitled) (Communications in Mathematical Research, 2021)
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).