The minimum sum of element orders of finite groups
Publish place: International Journal of Group Theory، Vol: 10، Issue: 2
Publish Year: 1400
نوع سند: مقاله ژورنالی
زبان: English
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تاریخ نمایه سازی: 14 اردیبهشت 1400
Abstract:
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 ۴.۶.۵ posed in [Group Theory and Computation, (۲۰۱۸) ۵۹-۹۰], 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.
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Authors
Maghsoud Jahani
Department of Mathematics, Shabestar Branch, Islamic Azad University, Shabestar, Iran
Yadollah Marefat
Department of Mathematics, Shabestar branch, Islamic Azad University, Shabestar, Iran
Hasan Refaghat
Department of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran
Bahram Vakili Fasaghandisi
Department of Mathematics, Shabestar branch, Islamic Azad University, Shabestar, Iran