Bott–Samelson theorem ($H_{\ast }(\Omega \Sigma X;\mathbb{Z})=T_{\mathbb{Z}}({\tilde{H}}_{\ast }(X;\mathbb{Z}))$)

For a connected based CW complex with free integral homology, the Pontryagin ring of its looped reduced suspension is the indicated tensor algebra. The generator inclusion comes from $X\to \Omega \Sigma X$, and multiplication corresponds to concatenation of words in the James reduced product.