A characterization of some finite simple groups by their character codegrees
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929699531259904 |
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| author | Tong-Viet, Hung P. |
| author_facet | Tong-Viet, Hung P. |
| contents | For a finite group $G$ and an irreducible complex character $χ$ of $G$, the codegree of $χ$ is defined by $\textrm{cod}(χ)=|G:\textrm{ker}(χ)|/χ(1)$, where $\textrm{ker}(χ)$ is the kernel of $χ$. In this paper, we show that if $H$ is a finite simple exceptional group of Lie type or a projective special linear group and $G$ is any finite group such that the character codegree sets of $G$ and $H$ coincide, then $G$ and $H$ are isomorphic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17794 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A characterization of some finite simple groups by their character codegrees Tong-Viet, Hung P. Group Theory Representation Theory 20C15, 20D05 For a finite group $G$ and an irreducible complex character $χ$ of $G$, the codegree of $χ$ is defined by $\textrm{cod}(χ)=|G:\textrm{ker}(χ)|/χ(1)$, where $\textrm{ker}(χ)$ is the kernel of $χ$. In this paper, we show that if $H$ is a finite simple exceptional group of Lie type or a projective special linear group and $G$ is any finite group such that the character codegree sets of $G$ and $H$ coincide, then $G$ and $H$ are isomorphic. |
| title | A characterization of some finite simple groups by their character codegrees |
| topic | Group Theory Representation Theory 20C15, 20D05 |
| url | https://arxiv.org/abs/2406.17794 |