On some series of a group related to the non-abelian tensor square of groups
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866912683980226560 |
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| author | Bastos, Raimundo de Oliveira, Ricardo Monetta, Carmine Rocco, Noraí |
| author_facet | Bastos, Raimundo de Oliveira, Ricardo Monetta, Carmine Rocco, Noraí |
| contents | Let $G$ be a group. We denote by $ν(G)$ a certain extension of the non-abelian tensor square $G \otimes G$ by $G \times G$. In this paper we prove that the derived subgroup $ν(G)'$ is a central product of three normal subgroups of $ν(G)$, all isomorphic to the non-abelian tensor square $G \otimes G$. As a consequence, we describe the structure of each term of the derived and lower central series of the group $ν(G)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_16366 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On some series of a group related to the non-abelian tensor square of groups Bastos, Raimundo de Oliveira, Ricardo Monetta, Carmine Rocco, Noraí Group Theory 20J06, 20F05, 20F14, 20D15 Let $G$ be a group. We denote by $ν(G)$ a certain extension of the non-abelian tensor square $G \otimes G$ by $G \times G$. In this paper we prove that the derived subgroup $ν(G)'$ is a central product of three normal subgroups of $ν(G)$, all isomorphic to the non-abelian tensor square $G \otimes G$. As a consequence, we describe the structure of each term of the derived and lower central series of the group $ν(G)$. |
| title | On some series of a group related to the non-abelian tensor square of groups |
| topic | Group Theory 20J06, 20F05, 20F14, 20D15 |
| url | https://arxiv.org/abs/2103.16366 |