The Hopf algebra structure of the cohomology of the 3-connective fibre space over the special unitary group (Q1570027)

Let \(\widetilde{\text{SU}}(n)\) be the 3-connective fibre space over \(\text{SU}(n)\), for \(n= 2,3,\dots, \infty\). Then \(\widetilde{\text{SU}}(n)\) is the Hopf space with an inverse since the product and the inverse of \(\text{SU}(n)\) induce the corresponding operations of \(\widetilde{\text{SU}} (n)\). The author determines \(H^* (\widetilde{\text{SU}} (n);\mathbb{F}_p)\) as a Hopf algebra over \({\mathcal A}_p\) the \(\operatorname {mod}p\) Steenrod algebra, where \(p\) is prime.