Guardat en:
| Autors principals: | , , , |
|---|---|
| Format: | Preprint |
| Publicat: |
2019
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| Matèries: | |
| Accés en línia: | https://arxiv.org/abs/1906.07830 |
| Etiquetes: |
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Taula de continguts:
- Let $G$ be a group. We denote by $ν(G)$ a certain extension of the non-abelian tensor square $[G,G^φ]$ by $G \times G$. We prove that if $G$ is a finite potent $p$-group, then $[G,G^φ]$ and the $k$-th term of the lower central series $γ_k(ν(G))$ are potently embedded in $ν(G)$ (Theorem A). Moreover, we show that if $G$ is a potent $p$-group, then the exponent $\exp(ν(G))$ divides $p \cdot \exp(G)$ (Theorem B). We also study the weak commutativity construction of powerful $p$-groups (Theorem C).