On Mimura's extension problem (Q1637176)

In the paper under review, the authors prove that the 23rd homotopy group of the exceptional Lie group \(G_{2}\) is equal to \(\mathbb{Z}_{4}\oplus \mathbb{Z}_{2}\). This result specifies the study of this homotopy group made by \textit{M. Mimura} [J. Math. Kyoto Univ. 6, 131--176 (1967; Zbl 0171.44101)]. As an application, the 23rd homotopy group of the Stiefel manifold \(V_{7,2}\) is also determined.