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We use combinatorial group theory methods to extend the definition of aclassical James-Hopf invariant to a simplicial group setting. This allow us torealize certain coalgebra idempotents at sSet -level and obtain a functorialdecomposition of the spectral sequence, associated with the lower p-centralseries filtration on the free simplicial group.

Simplicial James-Hopf map and decompositions of the unstable Adams spectral sequence for suspensions