Character degrees in principal blocks for distinct primes
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909664233390080 |
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| author | Bartelt, Annika |
| author_facet | Bartelt, Annika |
| contents | Let $G$ be a finite group of order divisible by two distinct primes $p$ and $q$. We show that $G$ possesses a non-trivial irreducible character of degree not divisible by $p$ nor $q$ lying in both the principal $p$- and $q$-block whenever $G$ is one of the following: an alternating group $\mathfrak{A}_n$, $n\geq 4$, a symmetric group $\mathfrak{S}_n$, $n\geq 3$, or a finite simple classical group of type A, B, or C, defined in characteristic distinct from $p$ and $q$. This extends earlier results of Navarro-Rizo-Schaeffer Fry for $2\in\{p,q\}$, and in particular completes the proof of an instance of a conjecture of the same authors, e.g., in the case of symmetric and alternating groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_06860 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Character degrees in principal blocks for distinct primes Bartelt, Annika Representation Theory Group Theory 20C15, 20C20, 20C30, 20C33 Let $G$ be a finite group of order divisible by two distinct primes $p$ and $q$. We show that $G$ possesses a non-trivial irreducible character of degree not divisible by $p$ nor $q$ lying in both the principal $p$- and $q$-block whenever $G$ is one of the following: an alternating group $\mathfrak{A}_n$, $n\geq 4$, a symmetric group $\mathfrak{S}_n$, $n\geq 3$, or a finite simple classical group of type A, B, or C, defined in characteristic distinct from $p$ and $q$. This extends earlier results of Navarro-Rizo-Schaeffer Fry for $2\in\{p,q\}$, and in particular completes the proof of an instance of a conjecture of the same authors, e.g., in the case of symmetric and alternating groups. |
| title | Character degrees in principal blocks for distinct primes |
| topic | Representation Theory Group Theory 20C15, 20C20, 20C30, 20C33 |
| url | https://arxiv.org/abs/2506.06860 |