A CRITERION FOR p-SOLVABILITY OF FINITE GROUPS, WHERE p = 7 OR 11

For a finite group G, define ψ´´(G) = ψ(G)/|G|², where ψ(G) = Σg∈Go(g) and o(g) denotes the order of g ∈ G. In this paper, we give a criterion for p-solvability by the function ψ´´, where p ∈ {7, 11}. We prove that if G is a finite group and ψ´´(G) ψ´´(PSL(2, p)), where p ∈ {7, 11}, then G is a p-solvable group.