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The v 1 -periodic homotopy groups v 1 #751 π. (X; p) are computed explicitly for all pairs (X, p), where X is an exceptional Lie group whose integral homology has no p-torsion. This yields new lower bounds for p-exponents of actual homotopy groups of these spaces. Delicate calculations with the unstable Novikov spectral sequence are required in the proof

𝑣₁-periodic homotopy groups of exceptional Lie groups: torsion-free cases