A simple, simply-connected, compact Lie group G is p-regular if it is homotopy equivalent to a product of spheres when localized at p. If A is the corresponding wedge of spheres, then it is well known that there is a p-local retraction of G off ΩΣA. We show that that complementary factor is very well behaved, and this allows us to deduce properties of G from those of ΩΣA. We apply this to show that, localized at p, the pth-power map on G is an H-map. This is a significant step forward in Arkowitz-Curjel and McGibbon's programme for identifying which power maps between finite H-spaces are H-maps.
Homology, Homotopy and Applications, Vol. 15 (2013), No. 2, pp.83-102.
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