Torsion in the cohomology of finite $H$-spaces

Abstract

We study torsion phenomena in the integral cohomologyof finite H-spaces X through the Eilenberg--Moore spectralsequence converging to H^*(Omega X;Z_{p}). We also investigatehow the difference between the Z_{p}-filtration lengthf_{p}(X) and the Z_{p}-cup length c_{p}(X) on a simply connected finiteH-space X is reflected in the Eilenberg--Moore spectralsequence converging to H^*(Omega X;Z_{p}). Finally we get thefollowing result: Let p be an odd prime and X ann--connected finite H--space with dim QH^{*}(X;Z_{p}) leq m. Then H^{*}(X;Z) is p--torsion free if pgeqfrac{m-1}{n}.