A new characterization of PSL(۲, ۲۵)

‎Let G be a finite group and \pi_{e}(G) be the set of element‎ ‎orders of G‎. ‎Let k \in \pi_{e}(G) and m_{k} be the number of‎ ‎elements of order k in G‎. ‎Set nse(G):=\{ m_{k} | k \in‎ ‎\pi_{e}(G)\}‎. ‎In this paper‎, ‎we prove that if G is a group such‎ ‎that nse(G)=nse(PSL(۲‎, ‎۲۵))‎, ‎then G \cong PSL(۲‎, ‎۲۵) ‎.

Keywords:

Element order , set of the numbers of elements of the same order , Sylow subgroup