A criterion for p-solvability of finite groups, where p=۷ or ۱۱

For a finite group G, define \psi^{\prime \prime}(G)=\psi(G)/|G|^۲ , where \psi(G)=\sum_{g\in G}o(g) and o(g) denotes the order of g \in G .  In this paper, we give a criterion for p-solvability by the function  \psi'', where p \in \{۷,  ۱۱\} . We prove that if G is a  finite group and \psi''(G)>\psi''({\rm PSL}(۲, p)), where p \in \{۷, ۱۱\}, then G is a p-solvable group.

کلیدواژه ها:

Finite group ، Sum of element orders ، p-solvable ، Function