Gottlieb groups of homogeneous spaces

In this paper, we compute the Gottlieb groups of the 2- dimensional sphere S 2 and give the lower bounds of the order of the kth Gottlieb subgroup of the quaternionic projective n-space H P n for some integers k. Moreover, we obtain some information of lower bounds or infinities of the order of the Gottlieb groups of various homogeneous spaces.