Normal 2-coverings in affine groups of small dimension
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866916853896445952 |
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| author | Fusari, Marco Previtali, Andrea Spiga, Pablo |
| author_facet | Fusari, Marco Previtali, Andrea Spiga, Pablo |
| contents | A finite group $G$ admits a normal $2$-covering if there exist two proper subgroups $H$ and $K$ with $G=\bigcup_{g\in G}H^g\cup\bigcup_{g\in G}K^g$. For determining inductively the finite groups admitting a normal $2$-covering, it is important to determine all finite groups $G$ possessing a normal $2$-covering, where no proper quotient of $G$ admits such a covering.
Using terminology arising from the O'Nan-Scott theorem, Garonzi and Lucchini have shown that these groups fall into four natural classes: product action, almost simple, affine and diagonal.
In this paper, we start a preliminary investigation of the affine case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_15610 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Normal 2-coverings in affine groups of small dimension Fusari, Marco Previtali, Andrea Spiga, Pablo Group Theory A finite group $G$ admits a normal $2$-covering if there exist two proper subgroups $H$ and $K$ with $G=\bigcup_{g\in G}H^g\cup\bigcup_{g\in G}K^g$. For determining inductively the finite groups admitting a normal $2$-covering, it is important to determine all finite groups $G$ possessing a normal $2$-covering, where no proper quotient of $G$ admits such a covering. Using terminology arising from the O'Nan-Scott theorem, Garonzi and Lucchini have shown that these groups fall into four natural classes: product action, almost simple, affine and diagonal. In this paper, we start a preliminary investigation of the affine case. |
| title | Normal 2-coverings in affine groups of small dimension |
| topic | Group Theory |
| url | https://arxiv.org/abs/2507.15610 |