Higher 𝑝-torsion in the 𝛽-family

Abstract

We prove the existence of new families of υ 2 {\upsilon _2} -periodic elements of the stable homotopy of the sphere detected in the second filtration of the Adams-Novikov Spectral Sequence for primes greater than 3. Our main corollary is that the p p -component of π ∗ s \pi _ * ^s contains any finite abelian p p -group as a subgroup in some dimension ( for p ≥ 5 ) ({\text {for}}p \geq 5) .