On exponent and nilpotency of [Ω(Sr+1),Ω(KPn)]

Abstract We give estimations of the nilpotency class and the p-primary exponent of the total Cohen groups [ Ω ( S r + 1 ) , Ω ( X ) ] especially, when X is the projective space over K = R , C , the field of reals or complex numbers and H , the quaternionic skew R -algebra.