Cohomology and the Combinatorics of Words for Magnus Formations

Ido Efrat

doi:10.48550/arXiv.2205.11933

Cohomology and the Combinatorics of Words for Magnus Formations

Ido Efrat

Department of Mathematics

Research output: Working paper/Preprint › Preprint

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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
DOIs	https://doi.org/10.48550/arXiv.2205.11933
State	Published - 24 May 2022

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math.NT

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10.48550/arXiv.2205.11933

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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-centraland p-Zassenhaus filtrations of G.

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Cohomology and the Combinatorics of Words for Magnus Formations

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