The codegree isomorphism problem for finite simple groups II
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917695009587200 |
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| author | Hung, Nguyen N. Moretó, Alexander |
| author_facet | Hung, Nguyen N. Moretó, Alexander |
| contents | Let $H$ be a nonabelian finite simple group. Huppert's conjecture asserts that if $G$ is a finite group with the same set of complex character degrees as $H$, then $G\cong H\times A$ for some abelian group $A$. Over the past two decades, several specific cases of this conjecture have been addressed. Recently, attention has shifted to the analogous conjecture for character codegrees: if $G$ has the same set of character codegrees as $H$, then $G\cong H$. Unfortunately, both problems have primarily been examined on a case-by-case basis. In this paper and the companion [HM22], we present a more unified approach to the codegree conjecture and confirm it for several families of simple groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_10398 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The codegree isomorphism problem for finite simple groups II Hung, Nguyen N. Moretó, Alexander Group Theory Representation Theory Let $H$ be a nonabelian finite simple group. Huppert's conjecture asserts that if $G$ is a finite group with the same set of complex character degrees as $H$, then $G\cong H\times A$ for some abelian group $A$. Over the past two decades, several specific cases of this conjecture have been addressed. Recently, attention has shifted to the analogous conjecture for character codegrees: if $G$ has the same set of character codegrees as $H$, then $G\cong H$. Unfortunately, both problems have primarily been examined on a case-by-case basis. In this paper and the companion [HM22], we present a more unified approach to the codegree conjecture and confirm it for several families of simple groups. |
| title | The codegree isomorphism problem for finite simple groups II |
| topic | Group Theory Representation Theory |
| url | https://arxiv.org/abs/2406.10398 |