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A criterion for $p$-solvability of finite groups, where $p=7$ or $11$ | ||
| Journal of Mahani Mathematical Research | ||
| دوره 13، شماره 2 - شماره پیاپی 27، آبان 2024، صفحه 225-231 اصل مقاله (506.7 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2024.22002.1488 | ||
| نویسنده | ||
| Sara Pouyandeh* | ||
| Department of Mathematics, Payamenoor University, Tehran, Iran | ||
| چکیده | ||
| For a finite group $G$, define $ \psi^{\prime \prime}(G)=\psi(G)/|G|^2 $, where $\psi(G)=\sum_{g\in G}o(g)$ and $o(g)$ denotes the order of $g \in G $. In this paper, we give a criterion for $p$-solvability by the function $\psi''$, where $ p \in \{7, 11\} $. We prove that if $ G $ is a finite group and $\psi''(G)>\psi''({\rm PSL}(2, p))$, where $p \in \{7, 11\}$, then $G$ is a $p$-solvable group. | ||
| کلیدواژه‌ها | ||
| Finite group؛ Sum of element orders؛ p-solvable؛ function | ||
| مراجع | ||
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