On two problems about order sequences of finite groups
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910700953141248 |
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| author | Lazorec, Mihai-Silviu |
| author_facet | Lazorec, Mihai-Silviu |
| contents | The order sequence of a finite group $G$ is a non-decreasing finite sequence formed of the element orders of $G$. Several properties of order sequences were studied by P. J. Cameron and H. K. Dey in a recent paper that concludes with a list of open problems. In this paper we solve two of these problems by showing the following facts: 1) if there is a non-supersolvable/non-solvable group of order $n$, it is not always true that its order sequence is properly dominated by the order sequence of any supersolvable/solvable group of order $n$; 2) the supersolvability of a finite group cannot be described by its order sequence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_10797 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On two problems about order sequences of finite groups Lazorec, Mihai-Silviu Group Theory The order sequence of a finite group $G$ is a non-decreasing finite sequence formed of the element orders of $G$. Several properties of order sequences were studied by P. J. Cameron and H. K. Dey in a recent paper that concludes with a list of open problems. In this paper we solve two of these problems by showing the following facts: 1) if there is a non-supersolvable/non-solvable group of order $n$, it is not always true that its order sequence is properly dominated by the order sequence of any supersolvable/solvable group of order $n$; 2) the supersolvability of a finite group cannot be described by its order sequence. |
| title | On two problems about order sequences of finite groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2411.10797 |