Homotopy nilpotency in \(p\)-regular loop spaces (Q846888)

The authors study the following problem: how far from being homotopy commutative is a loop space having the homotopy type of the \(p\)-completion of a product of a finite numbers of spheres. In particular, they determine the homotopy nilpotency explicitly for a \(p\)-localized compact simply connected simple Lie group and for an exotic \(p\)-compact group \(X\). To prove these results, they show a cohomological criterion for a Samelson product and they use this criterion.