Solvable and non-solvable finite groups of the same order type
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arXiv
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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912434144411648 |
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| author | Piwek, Paweł |
| author_facet | Piwek, Paweł |
| contents | We construct two finite groups of size $2^{365}\cdot 3^{105}\cdot 7^{104}$: a solvable group $G$ and a non-solvable group $H$, such that for every integer $n$ the groups have the same number of elements of order $n$. This answers a question posed in 1987 by John G. Thompson. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_02197 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Solvable and non-solvable finite groups of the same order type Piwek, Paweł Group Theory 20D10 We construct two finite groups of size $2^{365}\cdot 3^{105}\cdot 7^{104}$: a solvable group $G$ and a non-solvable group $H$, such that for every integer $n$ the groups have the same number of elements of order $n$. This answers a question posed in 1987 by John G. Thompson. |
| title | Solvable and non-solvable finite groups of the same order type |
| topic | Group Theory 20D10 |
| url | https://arxiv.org/abs/2403.02197 |