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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2304.10708 |
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| _version_ | 1866913579380244480 |
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| author | Sugimoto, Masahiro |
| author_facet | Sugimoto, Masahiro |
| contents | K. Harada conjectured for any finite group $G$, the product of sizes of all conjugacy classes is divisible by the product of degrees of all irreducible characters. We study this conjecture when $G$ is the general linear group over a finite field. We show the conjecture holds if the order of the field is sufficiently large. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_10708 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Harada's conjecture II for the finite general linear groups and unitary groups Sugimoto, Masahiro Group Theory 20C15 K. Harada conjectured for any finite group $G$, the product of sizes of all conjugacy classes is divisible by the product of degrees of all irreducible characters. We study this conjecture when $G$ is the general linear group over a finite field. We show the conjecture holds if the order of the field is sufficiently large. |
| title | Harada's conjecture II for the finite general linear groups and unitary groups |
| topic | Group Theory 20C15 |
| url | https://arxiv.org/abs/2304.10708 |