Let $X$ be a topological group. Let $\tau_1$ and $\tau_2$ representing elements of $\pi_n(X)$. Is it true that
$$ [\tau_1] [\tau_2] = [\tau_1 \tau_2] $$ in $\pi_n(X)$?,
where of course "$[\tau_1] [\tau_2]$" refers to the $\pi_n(X)$ group operation, and by $\tau_1 \tau_2$ I mean the map $S^n \ni x \mapsto \tau_1(x) \tau_2(x)$.
I know from greenberg harper algebraic topology a first course, page 30, that this is true for n=1.
It seems to me that the answer is a simple "yes", but I wonder why I can't find it on the internet.