Elena Di Domenico, Carmine Monetta, Marialaura Noce
Published 2022-05-24Version 1
Let $G$ be a finite group of order $n$, and denote by $\rho(G)$ the product of element orders of $G$. The aim of this work is to provide some upper bounds for $\rho(G)$ depending only on $n$ and on its least prime divisor, when $G$ belongs to some classes of non-cyclic groups.
On a bijection between a finite group to a non-cyclic group with divisibility of element orders
The Number of Finite Groups Whose Element Orders is Given
The solvability of a finite group by the sum of powers of element orders
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