On the sum of element orders of PSL(2, p) for some p

Let G be a finite group and psi(G) = Sigma(g subset of G) o(g), where o(g) denotes the order of g is an element of G. In this paper, we show that if G is a group of order vertical bar PSL(2, p)vertical bar, then psi(G) >= psi(PSL(2, p)), where p is an element of{11, 13, 19, 23, 29, 37, 61}. Also we prove that vertical bar G vertical bar = vertical bar PSL(2, p)vertical bar and psi(G) = psi(PSL(2, p)) if and only if G congruent to PSL(2, p), where p is an element of {11, 13, 19, 23, 29, 37, 61}. Furthermore, we prove that PSL(2, 17) is determined by its order and the sum of element orders.