The exponent of the non-abelian tensor square and related constructions of $p$-groups
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866917055649808384 |
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| author | Bastos, R. de Melo, E. Gonçalves, N. Monetta, C. |
| author_facet | Bastos, R. de Melo, E. Gonçalves, N. Monetta, C. |
| contents | Let $G$ be a finite $p$-group. In this paper we obtain bounds for the exponent of the non-abelian tensor square $G \otimes G$ and of $ν(G)$, which is a certain extension of $G \otimes G$ by $G \times G$. In particular, we bound $\exp(ν(G))$ in terms of $\exp(ν(G/N))$ and $\exp(N)$ when $G$ admits some specific normal subgroup $N$. We also establish bounds for $\exp(G \otimes G)$ in terms of $\exp(G)$ and either the nilpotency class or the coclass of the group $G$, improving some existing bounds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_10693 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | The exponent of the non-abelian tensor square and related constructions of $p$-groups Bastos, R. de Melo, E. Gonçalves, N. Monetta, C. Group Theory 20D15, 20E06, 20J06 Let $G$ be a finite $p$-group. In this paper we obtain bounds for the exponent of the non-abelian tensor square $G \otimes G$ and of $ν(G)$, which is a certain extension of $G \otimes G$ by $G \times G$. In particular, we bound $\exp(ν(G))$ in terms of $\exp(ν(G/N))$ and $\exp(N)$ when $G$ admits some specific normal subgroup $N$. We also establish bounds for $\exp(G \otimes G)$ in terms of $\exp(G)$ and either the nilpotency class or the coclass of the group $G$, improving some existing bounds. |
| title | The exponent of the non-abelian tensor square and related constructions of $p$-groups |
| topic | Group Theory 20D15, 20E06, 20J06 |
| url | https://arxiv.org/abs/2007.10693 |