Coprime commutators in finite groups
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2018
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| _version_ | 1866918182613155840 |
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| author | Monetta, Carmine Bastos, Raimundo |
| author_facet | Monetta, Carmine Bastos, Raimundo |
| contents | Let $G$ be a finite group and let $k \geq 2$. We prove that the coprime subgroup $γ_k^*(G)$ is nilpotent if and only if $|xy|=|x||y|$ for any $γ_k^*$-commutators $x,y \in G$ of coprime orders (Theorem A). Moreover, we show that the coprime subgroup $δ_k^*(G)$ is nilpotent if and only if $|ab|=|a||b|$ for any powers of $δ_k^*$-commutators $a,b\in G$ of coprime orders (Theorem B). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1811_10025 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Coprime commutators in finite groups Monetta, Carmine Bastos, Raimundo Group Theory Let $G$ be a finite group and let $k \geq 2$. We prove that the coprime subgroup $γ_k^*(G)$ is nilpotent if and only if $|xy|=|x||y|$ for any $γ_k^*$-commutators $x,y \in G$ of coprime orders (Theorem A). Moreover, we show that the coprime subgroup $δ_k^*(G)$ is nilpotent if and only if $|ab|=|a||b|$ for any powers of $δ_k^*$-commutators $a,b\in G$ of coprime orders (Theorem B). |
| title | Coprime commutators in finite groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/1811.10025 |