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Ido Efrat
Cohomology and the combinatorics of words for Magnus formations
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| Published: |
August 5, 2024. |
| Keywords: |
Profinite cohomology, combinatorics of words, Magnus formations, shuffle algebra, Lyndon words, shuffle relations, Massey products,
lower p-central filtration, p-Zassenhaus filtration. |
| Subject [2010]: |
Primary 12G05, Secondary 20J06, 68R15. |
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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 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.
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| Acknowledgements
This work was supported by the Israel Science Foundation (grant No. 569/21).
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| Author information
Ido Efrat
Earl Katz Family Chair in Pure Mathematics
Department of Mathematics
Ben-Gurion University of the Negev
P.O. Box 653, Be'er-Sheva 8410501, Israel
efrat@bgu.ac.il
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