Filtering the fiber of the pinch map

In [3], Cohen, Moore and Neisendorfer analyzed the homotopy type of the mod pr Moore space P2n+1 = S2n ∪pr e2n+1 by constructing a fibration sequence Ω2S2n+1 ∂n −→ ΩFn −→ ΩP2n+1 −→ ΩS2n+1. A key result is that both ΩFn and ΩP2n+1 contain a factor which is the loop space on a one point union of Moore spaces that are at least 4n − 2 connected. Removing this factor (which can be inductively considered later) leaves a fibration sequence: · · · → Ω2S2n+1 ∂ −→ Fn −→ T2n+1 −→ ΩS2n+1 and they show that Fn ∼= S2n−1 × ∏