Wreath products and the non-coprime $k(GV)$ problem
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909655091904512 |
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| author | Hung, Nguyen N. Maróti, Attila Madrid, Juan Martínez |
| author_facet | Hung, Nguyen N. Maróti, Attila Madrid, Juan Martínez |
| contents | Let $G = X \wr H$ be the wreath product of a nontrivial finite group $X$ with $k$ conjugacy classes and a transitive permutation group $H$ of degree $n$ acting on the set of $n$ direct factors of $X^n$. If $H$ is semiprimitive, then $k(G) \leq k^n$ for every sufficiently large $n$ or $k$. This result solves a case of the non-coprime $k(GV)$ problem and provides an affirmative answer to a question of Garzoni and Gill for semiprimitive permutation groups. The proof does not require the classification of finite simple groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20208 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Wreath products and the non-coprime $k(GV)$ problem Hung, Nguyen N. Maróti, Attila Madrid, Juan Martínez Group Theory Representation Theory Primary 20B05, 20E45 Let $G = X \wr H$ be the wreath product of a nontrivial finite group $X$ with $k$ conjugacy classes and a transitive permutation group $H$ of degree $n$ acting on the set of $n$ direct factors of $X^n$. If $H$ is semiprimitive, then $k(G) \leq k^n$ for every sufficiently large $n$ or $k$. This result solves a case of the non-coprime $k(GV)$ problem and provides an affirmative answer to a question of Garzoni and Gill for semiprimitive permutation groups. The proof does not require the classification of finite simple groups. |
| title | Wreath products and the non-coprime $k(GV)$ problem |
| topic | Group Theory Representation Theory Primary 20B05, 20E45 |
| url | https://arxiv.org/abs/2412.20208 |