Characterization of ${\rm Alt}(5) \times \mathbb{Z}_p$, where $p \in \{ 17, 23\}$, by their product element orders
نویسندگان
1 Department of Mathematics, Faculty of Science, University of Jiroft, Jiroft, Iran
2 Department of Mathematics, Faculty of Science, Emam Ali University, Tehran, Iran.
doi
10.22034/as.2023.3010چکیده
We denote the integer $ \prod_{g \in G} o(g) $ by $\psi^{\prime}(G)$ where $o(g)$ denotes the order of $g \in G$ and $G$ is a finite group. In [14], it was proved that some finite simple group can be uniquely determined by its product of element orders. In this paper, we characterize ${\rm Alt}(5) \times \mathbb{Z}_p$, where $p \in \{ 17, 23\}$, by their product of element orders.
