A New Characterization of PSL(2, q) for Some q - Asboei, A.K.; Amiri, S.S.S.; Iranmanesh, A. (Український математичний журнал, 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).