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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.

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