Centers and finite coverings of finite loop spaces.

@article{Notbohm1994CentersAF,
  title={Centers and finite coverings of finite loop spaces.},
  author={Dietrich Notbohm and J. M. Moller},
  journal={Journal f{\"u}r die reine und angewandte Mathematik (Crelles Journal)},
  year={1994},
  volume={1994},
  pages={134 - 99}
}
A finite loop space X is a triple (X, BX, e), in which e : X -> ΩΒΧ is an equivalence from the space X into the loop space ΩΒΧ of the pointed space BX. The loop space X is called finite if X is homotopy equivalent to a finite C W-complex or if the integral homology H χ (X; Z) is finitely generated s a graded abelian group. The latter condition is a little weaker, but sufficient for proving most of the nice results about finite loop spaces. 

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