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We present progress in trying to verify a long-standing conjecture by MarkMahowald on the $v_{1}$-periodic component of the classical Adams spectralsequence for a Moore space $M$. The approach we follow was proposed by JohnPalmieri in his work on the stable category of $A$-comodules. We improve onPalmieri's work by working with the endomorphism ring of $M$ - $End(M)$ thusresolving some of the initial difficulties of his approach and formulating aconjecture of our own that would lead to Mahowald's formulation.

On the $v_1$ periodicity of the Moore space