中文摘要：

　决定球面稳定同伦群是同伦论中的核心问题之一，是非常重要的．该文证明：球面稳定同伦元素а1β1βs是一个阶为P的非平凡元素，其中P≥5是任意奇素数，1≤s≤P．

英文摘要：

To determine the stable homotopy groups of spheres π＊S is one of the central problems in homotopy theory. In this paper, it is proved that, for p ≥ 5 to be an arbitrary odd prime number and 1 ≤ s 〈 p, the homotopy element а1β1βs is nontrivial and of order p in the stable homotopy groups of spheres π＊S.