THE p-ZASSENHAUS FILTRATION of A FREE PROFINITE GROUP and SHUFFLE RELATIONS

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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 p-Zassenhaus filtration of S. For p > n, we give a word-combinatorial description of the cohomology group H2 (S/Sn,p),ℤ/p) in terms of the shuffle algebra on X. We give a natural linear basis for this cohomology group, which is constructed by means of unitriangular representations arising from Lyndon words.

Original languageEnglish
JournalJournal of the Institute of Mathematics of Jussieu
DOIs
StateAccepted/In press - 1 Jan 2021

Keywords

  • Galois cohomology
  • Massey products
  • modular dimension subgroups
  • p-Zassenhaus filtration
  • shuffle algebra
  • shuffle relations

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