Structural Results On The Weak Commutativity Construction
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913893696143360 |
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| author | Ortega, Guilherme Bastos, Raimundo de Oliveira, Ricardo |
| author_facet | Ortega, Guilherme Bastos, Raimundo de Oliveira, Ricardo |
| contents | The weak commutativity group $χ(G)$ is generated by two isomorphic groups $G$ and $G^{φ}$ subject to the relations $[g,g^φ]=1$ for all $g \in G$. We obtain new expressions for the terms of the derived series and the lower central series of $χ(G)$. We also present new bounds for the exponent of some sections of $χ(G)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_12146 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Structural Results On The Weak Commutativity Construction Ortega, Guilherme Bastos, Raimundo de Oliveira, Ricardo Group Theory 20E06, 20F05, 20F14, 20F50 The weak commutativity group $χ(G)$ is generated by two isomorphic groups $G$ and $G^{φ}$ subject to the relations $[g,g^φ]=1$ for all $g \in G$. We obtain new expressions for the terms of the derived series and the lower central series of $χ(G)$. We also present new bounds for the exponent of some sections of $χ(G)$. |
| title | Structural Results On The Weak Commutativity Construction |
| topic | Group Theory 20E06, 20F05, 20F14, 20F50 |
| url | https://arxiv.org/abs/2506.12146 |