**MSC:**- 55P35 Loop spaces
- 55T20 Eilenberg-Moore spectral sequences, See also {57T35}
- 57T15 Homology and cohomology of homogeneous spaces of Lie groups
- 57T35 Applications of Eilenberg-Moore spectral sequences, See also {55R20, 55T20}

as an application we show, that under certain conditions the cohomology of

a homogeneous space of a connected finite loop space with a maximal rank torsion

free subgroup is concentrated in even degrees and torsionfree, generalizing

classical theorems for compact Lie groups of Borel and Bott.

F. Neumann: On the Cohomology of Homogeneous Spaces of Finite Loop Spaces

and the Eilenberg-Moore Spectral Sequence,

Journal of Pure and Appl. Algebra