\(J\)-groups of the suspensions of the stunted lens spaces \(\text{mod }2p\) (Q1324957)

Let \(L^ m_ q\) denote the standard lens space \(S^{2n + 1} /Z_ q \bmod q\). In this paper the author determines the structures of (1) the KO-groups \(\text{KO}(S^ j (L^ m_ s /L^ n_ s))\), \(s = 2^ r\), for \(q \equiv 1 \bmod 2\), \(j \equiv 0 \bmod 2\), \(m > n\) and \(r > 0\); (2) the \(J\)-groups \(J(S^ j (L^ m_ s /L^ m_ s))\), \(s = 2^ r\), for \(q \equiv 1 \bmod 2\), \(j \equiv 0 \bmod 2\), \(m > n\) and \(r > 0\); (3) the \(J\)-groups \(J(S^ j (L^ m_ 2 /L^ m_{2p}))\), for odd prime \(p\), \(j \equiv 0 \bmod 2\), and \(m > n\); and obtains (4) the necessary inequalities between \(t\), \(m\) and \(n\) for the stable periodicity \(L^ m_{2p} /L^ n_{2p} \approx L^{m + t}_{2p} / L^{n + t}_{2p}\).