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We characterize H-spaces which are p-torsion Postnikov pieces of finite type by a cohomological property together with a necessary acyclicity condition. When the mod p cohomology of an H-space is finitely generated as an algebra over the Steenrod algebra we prove that its homotopy groups behave like those of a finite complex. In particular, a p-complete infinite loop space has a finite number of non-trivial homotopy groups if and only if its mod p cohomology satisfies this finiteness condition.
Published Online: 2007-06-14
Published in Print: 2007-05-23
© Walter de Gruyter