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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2411.08581 |
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| _version_ | 1866912117801615360 |
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| author | Lewis, Mark L. Martin, Brandon |
| author_facet | Lewis, Mark L. Martin, Brandon |
| contents | Let $G$ be a finite group, and let $d$ be the degree of an irreducible character of $G$ such that $|G|=d(d+e)$ for some $e>1$. Consider the case when $G$ is solvable, $d$ is square-free, and $(d,d+e)=1$. We wish to explore an equivalent condition on $G$ when $d\in\text{cd}(G)$. We show that if $d\in\text{cd}(G)$ then there is a sequence of congruences relating the prime power factors of $d+e$ to the product of prime factors of $d$ such that the product of the moduli in this sequence of congruences is $d$. Moreover, the argument will hold in both directions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_08581 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Groups with a Fixed Character Degree Lewis, Mark L. Martin, Brandon Group Theory 20C15 Let $G$ be a finite group, and let $d$ be the degree of an irreducible character of $G$ such that $|G|=d(d+e)$ for some $e>1$. Consider the case when $G$ is solvable, $d$ is square-free, and $(d,d+e)=1$. We wish to explore an equivalent condition on $G$ when $d\in\text{cd}(G)$. We show that if $d\in\text{cd}(G)$ then there is a sequence of congruences relating the prime power factors of $d+e$ to the product of prime factors of $d$ such that the product of the moduli in this sequence of congruences is $d$. Moreover, the argument will hold in both directions. |
| title | Groups with a Fixed Character Degree |
| topic | Group Theory 20C15 |
| url | https://arxiv.org/abs/2411.08581 |