On products of some \(\beta\)-elements in the homotopy of the \(\mod 3\) Moore spectrum (Q1378309)

\textit{S. Pemmaraju}, in his still unpublished thesis, showed the existence of \(v_2\)-periodic elements \(\beta_s\) and \(\beta_s'\) in the 3-primary stable homotopy groups of the sphere and Moore spectrum \(M\) for \(s\equiv 0\), 1, 2, 5 or 6 mod 9. Under the assumption of Pemmaraju's results, the authors of this paper prove that certain products \(\beta_s' \beta_t\) and \(\beta_s' \beta_t'\) are nonzero in \(\pi_*M\), by using the results of their earlier paper [Hiroshima Math. J. 26, No. 2, 415-431 (1996; Zbl 0869.55010)] and by showing that these products are nonzero in the \(E_2\)-term of the Adams-Novikov spectral sequence.