Cohomology and the Combinatorics of Words for Magnus Formations
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2022
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916079956131840 |
|---|---|
| author | Efrat, Ido |
| author_facet | Efrat, Ido |
| contents | 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 $H^2(G/G^Φ)$ combinatorically, in terms of the shuffle algebra on $X$. This partly extends existing results for the lower $p$-central and $p$-Zassenhaus filtrations of $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_11933 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Cohomology and the Combinatorics of Words for Magnus Formations Efrat, Ido Number Theory 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 $H^2(G/G^Φ)$ combinatorically, in terms of the shuffle algebra on $X$. This partly extends existing results for the lower $p$-central and $p$-Zassenhaus filtrations of $G$. |
| title | Cohomology and the Combinatorics of Words for Magnus Formations |
| topic | Number Theory |
| url | https://arxiv.org/abs/2205.11933 |