The character degree product and the conjugacy length product for finite general linear groups
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910775349608448 |
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| author | Hida, Akihiko Sugimoto, Masahiro |
| author_facet | Hida, Akihiko Sugimoto, Masahiro |
| contents | Let $G$ be a finite group. K. Harada conjectured that the product of degrees of all irreducible characters of $G$ divides the product of lengths of all conjugacy classes of $G$. We verify this conjecture for finite general linear groups and finite unitary groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03527 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The character degree product and the conjugacy length product for finite general linear groups Hida, Akihiko Sugimoto, Masahiro Representation Theory Group Theory 20C15 Let $G$ be a finite group. K. Harada conjectured that the product of degrees of all irreducible characters of $G$ divides the product of lengths of all conjugacy classes of $G$. We verify this conjecture for finite general linear groups and finite unitary groups. |
| title | The character degree product and the conjugacy length product for finite general linear groups |
| topic | Representation Theory Group Theory 20C15 |
| url | https://arxiv.org/abs/2501.03527 |