There is a product decomposition of a compact connected Lie group G at the prime p, called the mod p decomposition, when G has no p-torsion in homology. Then in studying the multiplicative structure of the p-localization of G, the Samelson products of the factor space inclusions of the mod p decomposition are fundamental. This paper determines (non-)triviality of these fundamental Samelson products in the p-localized exceptional Lie groups when the factor spaces are of rank ≤ 2, that is, G is quasi-p-regular.
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