On the nilpotence order of β1

Abstract

For p > 2, is the first positive even-dimensional element in the stable homotopy groups of spheres. A classical theorem of Nishida[1] states that all elements of positive dimension in the stable homotopy groups of spheres are nilpotent. In fact, Toda [4] proved . For p = 3 he showed that while . In [2] the second author computed the first thousand stems of the stable homotopy groups of spheres at the prime 5. One of the consequences of this computation is that while .