Izvorni znanstveni članak

https://doi.org/10.3336/gm.58.2.10

On groups with average element orders equal to the average element order of the alternating group of degree \(5\)

Marcel Herzog ; School of Mathematical Sciences, Tel-Aviv University, Ramat-Aviv, Tel-Aviv, Israel
Patrizia Longobardi ; Dipartimento di Matematica, Università di Salerno, via Giovanni Paolo II, 132, 84084 Fisciano (Salerno), Italy
Mercede Maj ; Dipartimento di Matematica, Università di Salerno, via Giovanni Paolo II, 132, 84084 Fisciano (Salerno), Italy

Preuzmi JATS datoteku

Sažetak

Let \(G\) be a finite group. Denote by \(\psi(G)\) the sum
\(\psi(G)=\sum_{x\in G}|x|,\) where \(|x|\) denotes the order of the element \(x\), and
by \(o(G)\) the average element orders, i.e. the quotient \(o(G)=\frac{\psi(G)}{|G|}.\)
We prove that \(o(G) = o(A_5)\) if and only if \(G \simeq A_5\), where \(A_5\) is the alternating group of degree \(5\).

Ključne riječi

Group element orders, alternating group

Hrčak ID:

312017

URI

https://hrcak.srce.hr/312017

Datum izdavanja:

22.12.2024.

Posjeta: 441 *