On two problems about order sequences of finite groups
| Autor: | Lazorec, Mihai-Silviu |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 10 pages |
| Databáze: | arXiv |
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