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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2511.13902 |
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| _version_ | 1866918206898176000 |
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| author | Jensen, Sara Lewis, Mark L. |
| author_facet | Jensen, Sara Lewis, Mark L. |
| contents | Let $G$ be a group, let $d$ be a character degree, and let $e$ be the integer so that $|G| = d(d+e)$. It has been shown when $e > 1$ that $|G| \le e^4 - e^3$. In this paper, we consider the groups where $|G| = e^4 - e^3$. It is known that $e$ must be a power of a prime. We classify the groups where $e$ is a prime and where $e$ is $4$, $9$, and $25$. In so doing, we find a new nonsolvable Camina pair. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_13902 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Groups Having a Character of Maximal Degree Jensen, Sara Lewis, Mark L. Group Theory 20C15 Let $G$ be a group, let $d$ be a character degree, and let $e$ be the integer so that $|G| = d(d+e)$. It has been shown when $e > 1$ that $|G| \le e^4 - e^3$. In this paper, we consider the groups where $|G| = e^4 - e^3$. It is known that $e$ must be a power of a prime. We classify the groups where $e$ is a prime and where $e$ is $4$, $9$, and $25$. In so doing, we find a new nonsolvable Camina pair. |
| title | Groups Having a Character of Maximal Degree |
| topic | Group Theory 20C15 |
| url | https://arxiv.org/abs/2511.13902 |