Character covering number of $\mathrm{PSL}_2 (q)$
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917591239360512 |
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| author | Arvind, Namrata Panja, Saikat |
| author_facet | Arvind, Namrata Panja, Saikat |
| contents | For a group $G$ and a character $χ$ of $G$, let $c(χ)$ denote the set of all irreducible characters of $G$, occurring in $χ$. We prove that whenever $q\geq 8$, all non-trivial irreducible character $χ$ of $\mathrm{PSL}_2(q)$ satisfies $c(χ^4)=\mathrm{Irr}\left(\mathrm{PSL}_2(q)\right)$ if $q=2^{2m+1}$ and $c(χ^3)=\mathrm{Irr}\left(\mathrm{PSL}_2(q)\right)$ otherwise. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_10467 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Character covering number of $\mathrm{PSL}_2 (q)$ Arvind, Namrata Panja, Saikat Group Theory Representation Theory 20C15, 20C33 For a group $G$ and a character $χ$ of $G$, let $c(χ)$ denote the set of all irreducible characters of $G$, occurring in $χ$. We prove that whenever $q\geq 8$, all non-trivial irreducible character $χ$ of $\mathrm{PSL}_2(q)$ satisfies $c(χ^4)=\mathrm{Irr}\left(\mathrm{PSL}_2(q)\right)$ if $q=2^{2m+1}$ and $c(χ^3)=\mathrm{Irr}\left(\mathrm{PSL}_2(q)\right)$ otherwise. |
| title | Character covering number of $\mathrm{PSL}_2 (q)$ |
| topic | Group Theory Representation Theory 20C15, 20C33 |
| url | https://arxiv.org/abs/2402.10467 |