TY - JOUR
T1 - THE p-ZASSENHAUS FILTRATION of A FREE PROFINITE GROUP and SHUFFLE RELATIONS
AU - Efrat, Ido
N1 - Funding Information:
I thank the referee for his/her comments and helpful suggestions. This research was supported by the Israel Science Foundation (grant 569/21).
Publisher Copyright:
© The Author(s), 2021. Published by Cambridge University Press.
PY - 2021/1/1
Y1 - 2021/1/1
N2 - 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.
AB - 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.
KW - Galois cohomology
KW - Massey products
KW - modular dimension subgroups
KW - p-Zassenhaus filtration
KW - shuffle algebra
KW - shuffle relations
UR - http://www.scopus.com/inward/record.url?scp=85116526987&partnerID=8YFLogxK
U2 - 10.1017/S1474748021000426
DO - 10.1017/S1474748021000426
M3 - Article
AN - SCOPUS:85116526987
JO - Journal of the Institute of Mathematics of Jussieu
JF - Journal of the Institute of Mathematics of Jussieu
SN - 1474-7480
ER -