A New Characterization of PSL(2, q) for Some q - Amiri, S. S. S.; Asboei, A. K.; Iranmanesh, A. (Ukrains’kyi Matematychnyi Zhurnal, 2015)
Let G be a finite group and let π_e (G) be the set of orders of elements from G. Let k ∈ π_e (G) and let m_k be the number of elements of order k in G. We set nse (G) := {m_k | k ∈ π_e (G)}. It is proved that PSL(2, q) are uniquely determined by nse (PSL(2, q)), where q ∈ {5, 7, 8, 9, 11, 13}. As the main result of the paper, we prove that if G is a group such that nse (G) = nse (PSL(2, q)), where q ∈ 16, 17, 19, 23, then G ≅ PSL(2, q).