Cosets of normal subgroups and union of two conjugacy classes
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913980606316544 |
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| author | Beltrán, Antonio |
| author_facet | Beltrán, Antonio |
| contents | Let $G$ be a finite group, $N$ a normal subgroup of $G$ and $x\in G-N$. We discuss when the coset $Nx$ is contained in the union of two conjugacy classes, $K$ and $D$, of $G$. We show that $N$ need not be solvable, and can even be non-abelian simple, but in these cases, $K$ and $D$ must have the same cardinality, and the non-solvable structure of $N$ is restricted. The non-abelian principal factors of $G$ contained in $N$ are then isomorphic to $S\times \cdots\times S$, where $S$ is a simple group of Lie type of odd characteristic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_06367 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cosets of normal subgroups and union of two conjugacy classes Beltrán, Antonio Group Theory Let $G$ be a finite group, $N$ a normal subgroup of $G$ and $x\in G-N$. We discuss when the coset $Nx$ is contained in the union of two conjugacy classes, $K$ and $D$, of $G$. We show that $N$ need not be solvable, and can even be non-abelian simple, but in these cases, $K$ and $D$ must have the same cardinality, and the non-solvable structure of $N$ is restricted. The non-abelian principal factors of $G$ contained in $N$ are then isomorphic to $S\times \cdots\times S$, where $S$ is a simple group of Lie type of odd characteristic. |
| title | Cosets of normal subgroups and union of two conjugacy classes |
| topic | Group Theory |
| url | https://arxiv.org/abs/2508.06367 |