Abstract: This paper proves the existence of third periodicity
element in the stable homotopy of spheres which is of order p
and is represented by in the term of the Adams-Novikov spectral
sequence. On the way of providing the main result, a new family in the stable
homotopy groups of which is represented by in the term of the classical Adams
spectral sequence also is detected, where and
Keywords and phrases: stable homotopy of spheres, Adams spectral sequence, Toda spectrum.
