Characterization of {\rm Alt}(۵) \times \mathbb{Z}_p, where p \in \{ ۱۷, ۲۳\}, by their product element orders

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 [۱۴], 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}(۵) \times \mathbb{Z}_p, where p \in \{ ۱۷, ۲۳\}, by their product of element orders.

کلیدواژه ها:

Finite group ، Hall subgroup ، Product of element orders ، Solvable group