Expansion of normal subsets of odd-order elements in finite groups
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911049232416768 |
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| author | Parker, Chris Saunders, Jack |
| author_facet | Parker, Chris Saunders, Jack |
| contents | Let $G$ be a finite group and $K$ a normal subset consisting of odd-order elements. The rational closure of $K$, denoted $\mathbf D_K$, is the set of elements $x \in G$ with the property that $\langle x \rangle = \langle y \rangle$ for some $y$ in $K$. If $K^2 \subseteq \mathbf D_K$, we prove that $\langle K \rangle$ is soluble. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_07529 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Expansion of normal subsets of odd-order elements in finite groups Parker, Chris Saunders, Jack Group Theory 20E45 (Primary) Let $G$ be a finite group and $K$ a normal subset consisting of odd-order elements. The rational closure of $K$, denoted $\mathbf D_K$, is the set of elements $x \in G$ with the property that $\langle x \rangle = \langle y \rangle$ for some $y$ in $K$. If $K^2 \subseteq \mathbf D_K$, we prove that $\langle K \rangle$ is soluble. |
| title | Expansion of normal subsets of odd-order elements in finite groups |
| topic | Group Theory 20E45 (Primary) |
| url | https://arxiv.org/abs/2507.07529 |