The validity of a Thompsons problem for $\rm{PSL(4,7)}$
| Autor: | Behrooz Khosravi, Cyrus Kalantarpour |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | AUT Journal of Mathematics and Computing, Vol 1, Iss 1, Pp 89-94 (2020) |
| Druh dokumentu: | article |
| ISSN: | 2783-2449 2783-2287 |
| DOI: | 10.22060/ajmc.2019.16174.1022 |
| Popis: | Let $\pi_e(G)$ be the set of elements orders of $G$. Also let $s_n$ be the number of elements of order $n$ in $G$ and ${\rm nse}(G)=\{s_n| n\in\pi_e(G)\}$. In this paper we prove that if $G$ is a group such that ${\rm nse}(G)= {\rm nse}(\rm PSL(4,7))$, $19\big\vert|G|$ and $19^2\nmid|G|$, then $G\cong{\rm PSL(4,7)}$. As a consequence of this result it follows that Thompson's problem is satisfied for the simple group $\rm{PSL(4,7)}$. |
| Databáze: | Directory of Open Access Journals |
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