The author studies the quotient group $¥mathscr{E}$(SO(4))/$¥mathscr{E}$#(SO(4)), where $¥mathscr{E}$(SO(4)) is the group of homotopy classes of self homotopy equivalences of the rotation group SO(4) and $¥mathscr{E}$#(SO(4)) is the subgroup of it consisting of elements that induce the identity on homotopy groups.
