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| Main Authors: | , |
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| 格式: | Preprint |
| 出版: |
2018
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| 主題: | |
| 在線閱讀: | https://arxiv.org/abs/1811.10025 |
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書本目錄:
- 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).