Freudenthal suspension theorem

This fact is related to: homotopy groups

Statement

Let $X$ be a $(n-1)$-connected space having a nondegenerate basepoint $x_{0}$. Then the suspension homomorphism from $\pi _{q}(X)\to \pi _{q+1}(X)$ is an isomorphism for $q\leq 2n-2$ and is surjective for $q=2n-1$.