Simple Bψ-groups

In a finite group G, ψ (G ) denotes the sum of element orders of G. A finite group G is said to be a B_ψ-group if ψ (H )<|G | for any proper subgroup H of G. In Lazorec (Rev Real Acad Cienc Exact Fis Nat Ser A Mat 117:448, 2023), Lazorec put forward the following question: Question. What can be said about the B_ψ property of the finite simple groups PSL(2 ,q ) ? In this paper, we show that if S is a finite simple group, such that S ≠A l t (n ) for any n ≥14 , then S is a B_ψ-group.