Cohomology and the combinatorics of words for Magnus formations

Ido Efrat

Cohomology and the combinatorics of words for Magnus formations

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	1177-1195
Number of pages	19
Journal	New York Journal of Mathematics
Volume	30
State	Published - 1 Jan 2024

Keywords

Lyndon words
Magnus formations
Massey products
Profinite cohomology
combinatorics of words
lower p-central filtration
p-Zassenhaus filtration
shuffle algebra
shuffle relations

ASJC Scopus subject areas

General Mathematics

Cite this

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AB - For a prime number p and a free pro-p group G on a totally ordered basis X, we consider closed normal subgroups GΦ 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∕GΦ) 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.

KW - Lyndon words

KW - Magnus formations

KW - Massey products

KW - Profinite cohomology

KW - combinatorics of words

KW - lower p-central filtration

KW - p-Zassenhaus filtration

KW - shuffle algebra

KW - shuffle relations

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JO - New York Journal of Mathematics

JF - New York Journal of Mathematics

ER -

Cohomology and the combinatorics of words for Magnus formations

Abstract

Keywords

ASJC Scopus subject areas

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