MAXIMUM SUM ELEMENT ORDERS OF ALL PROPER SUBGROUPS OF PGL(2,Q)

For a finite group G, Let Ã(G) denote the sum of element orders of G. Here, we show that if q is a power of a odd prime p , then the projective special linear group PSL(2, q) has maximum sum element orders among all proper subgroups of projective general linear group PGL(2, q).