The Action of the Steenrod Algebra on the Cohomology of $p$-Compact Groups

Abstract

In the present paper, we determine the action of the Steenrod operations on the cohomology of simply connected $p$-compact groups with no $p$-torsion in the integral homologies for an odd prime $p$. To do so we study simple simply connected $p$-compact groups since any simply connected $p$-compact group with no $p$-torsion in the integral homology is a product of such $p$-compact groups.