The lower p-central series of a free profinite group and the shuffle algebra

2018/08/16 by Efrat, Ido
#12E30 #12F10 #FOS: Mathematics #K-Theory and Homology (math.KT) #Number Theory (math.NT) #Primary 12G05 #Rings and Algebras (math.RA) #Secondary 68R15

paper · doi:10.48550/arxiv.1808.05354

Abstract

For a prime number p and a free profinite group S on the basis X, let S^(n,p), n=1,2,… be the lower p-central filtration of S. For p>n, we give a combinatorial description of H²(S/S^(n,p),ℤ/p) in terms of the Shuffle algebra on X.

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