\(J\)-groups of the quaternionic spherical space forms (Q1336501)

Let \(Q_ m\) \((m \geq 2)\) be the subgroup of the unit sphere \(S^ 3\) in the quaternion field \(H\) generated by the two elements \(x = \exp (\pi i/2^{m - 1})\) and \(y = j\). The action of \(Q_ m\) on the unit sphere \(S^{4n + 3}\) in the quaternion \((n + 1)\)-space is given by the diagonal action. Let \(N^ n (m)\) denote the quotient manifold \(S^{4n + 3}/Q_ m\). Using the orthogonal representation ring \(RO (Q_ m)\) and the additive structure of \(\widetilde {KO} (N^ n (m))\) the author determines the structure of the reduced \(J\)-group \(\widetilde J(N^ n (m))\) for all \(m \geq 2\).