On One Application of Asphericity of Presentations
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918003848773632 |
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| author | Zykin, Maxim |
| author_facet | Zykin, Maxim |
| contents | I present a direct proof of Lemma 3(a) from O. V. Kulikova's work on torsion in the group $F/[M,N]$, using only Proposition 1.2 of Chiswell-Collins-Huebschmann on combinatorially aspherical presentations. In particular, I show that if two presentations satisfy the RC condition and are combinatorially aspherical, then the quotient $N/[F,N]$ is free abelian on the defining relators and central in $F/[F,N]$, whence the extension $F/[M,N]$ is torsion-free. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_20210 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On One Application of Asphericity of Presentations Zykin, Maxim Group Theory I present a direct proof of Lemma 3(a) from O. V. Kulikova's work on torsion in the group $F/[M,N]$, using only Proposition 1.2 of Chiswell-Collins-Huebschmann on combinatorially aspherical presentations. In particular, I show that if two presentations satisfy the RC condition and are combinatorially aspherical, then the quotient $N/[F,N]$ is free abelian on the defining relators and central in $F/[F,N]$, whence the extension $F/[M,N]$ is torsion-free. |
| title | On One Application of Asphericity of Presentations |
| topic | Group Theory |
| url | https://arxiv.org/abs/2504.20210 |