Cohomology and the Combinatorics of Words for Magnus Formations

2022/05/24 by Efrat, Ido
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2205.11933

Abstract

For a prime number p and a free pro-p group G on a totally ordered basis X, we consider closed normal subgroups G^Φ of G which are generated by p-powers of iterated commutators associated with Lyndon words in the alphabet X. We express the profinite cohomology group H²(G/G^Φ) combinatorically, in terms of the shuffle algebra on X. This partly extends existing results for the lower p-central and p-Zassenhaus filtrations of G.

Related

• The p-Zassenhaus Filtration of a Free Profinite Group and Shuffle Relations
• The Cohomology of canonical quotients of free groups and Lyndon words
• The lower p-central series of a free profinite group and the shuffle algebra
• Filtrations of free groups arising from the lower central series
• The Zassenhaus filtration, Massey Products, and Representations of Profinite Groups