Homotopy nilpotency of some homogeneous spaces

Abstract Let $${\mathbb {K}}={\mathbb {R}},\,{\mathbb {C}}$$ K = R , C , the field of reals or complex numbers and {H}}$$ H skew {R}}$$ -algebra quaternions. We study homotopy nilpotency loop spaces $$\Omega (G_{n,m}({\mathbb {K}}))$$ Ω ( G n m ) (F_{n;n_1,\ldots ,n_k}({\mathbb F ; 1 … k (V_{n,m}({\mathbb V Grassmann $$G_{n,m}({\mathbb {K}})$$ flag $$F_{n;n_1,\ldots Stiefel $$V_{n,m}({\mathbb manifolds. Additionally, classes p -localized (G^+_{n,m}({\mathbb {K}})_{(p)})$$ + p for certain primes are estimated, where $$G^+_{n,m}({\mathbb {K}})_{(p)}$$ is oriented Further, localized homogeneous given as quotients exceptional Lie groups investigated well.