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.
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Yutaka Hemmi, Hirokazu Nishinobu, Kuniyuki Ogi, The Action of the Steenrod Algebra on the Cohomology of <em>p</em>-Compact Groups. Publ. Res. Inst. Math. Sci. 44 (2008), no. 4, pp. 1199–1218DOI 10.2977/PRIMS/1231263784