The cohomology rings of homogeneous spaces

Let $G$ be a compact connected Lie group and $K$ closed subgroup. Assume that the order of any torsion element in integral cohomology is invertible given principal ideal domain $k$. It known this case homogeneous space $G/K$ with coefficients $k$ product $H^{*}(BK)$ over $H^{*}(BG)$ are isomorphic as $k$-modules. We show isomorphism multiplicative natural pair $(G,K)$ provided 2 The proof uses homotopy Gerstenhaber algebras an essential way. In particular, we normalized singular cochains on classifying torus formal algebra.