A characterization of $A_5$ by its average order

Tarnauceanu, Marius

doi:10.22108/ijgt.2023.138637.1866

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	A characterization of $A_5$ by its average order
International Journal of Group Theory
مقاله 2، دوره 14، شماره 3، آذر 2025، صفحه 117-123 اصل مقاله (427.14 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/ijgt.2023.138637.1866
نویسنده
Marius Tarnauceanu^*
Faculty of Mathematics, "Al.I. Cuza" University of Iasi
چکیده
Let $o(G)$ be the average order of a finite group $G$. M. Herzog, P. Longobardi and M. Maj [M. Herzog, P. Longobardi and M. Maj, Another criterion for solvability of finite groups, J. Algebra, 597 (2022) 1-23.] showed that if $G$ is non-solvable and $o(G)=o(A_5)$, then $G\cong A_5$. In this note, we prove that the equality $o(G)=o(A_5)$ does not hold for any finite solvable group $G$. Consequently, up to isomorphism, $A_5$ is determined by its average order.
کلیدواژه‌ها
average order؛ sum of element orders؛ solvable group

مراجع
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A characterization of $A_5$ by its average order