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The minimum sum of element orders of finite groups | ||
| International Journal of Group Theory | ||
| مقاله 1، دوره 10، شماره 2، شهریور 2021، صفحه 55-60 اصل مقاله (184.7 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2019.115910.1538 | ||
| نویسندگان | ||
| Maghsoud Jahani1؛ Yadollah Marefat* 2؛ Hasan Refaghat3؛ Bahram Vakili Fasaghandisi2 | ||
| 1Department of Mathematics, Shabestar Branch, Islamic Azad University, Shabestar, Iran | ||
| 2Department of Mathematics, Shabestar branch, Islamic Azad University, Shabestar, Iran | ||
| 3Department of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran | ||
| چکیده | ||
| Let $ G $ be a finite group and \( \psi(G)=\sum_{g\in G}o(g) \), where $ o(g) $ denotes the order of $g\in G$. We show that the Conjecture 4.6.5 posed in [Group Theory and Computation, (2018) 59-90], is incorrect. In fact, we find a pair of finite groups $G$ and $S$ of the same order such that $ \psi(G)<\psi(S)$, with $G$ solvable and $S$ simple. | ||
| کلیدواژه‌ها | ||
| Finite group؛ element orders sum؛ solvable group؛ simple group | ||
| مراجع | ||
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