A remark on the second homotopy groups of compact Riemannian 3-symmetric spaces

In order to calculate the second Stiefel-Whitney class of a 1-connected compact Riemannian 3-symmetric space G/K by BorelHirzebruch's method, we have to know the second cohomology group H2{G/K, Z2) = Hom(n2(G/K), Z2). In this paper, we shall describe precisely the connected Lie subgroup K and calculate explicitly the second homotopy group x2(G/K) in terms of the roots of G.