A nilpotency criterion for finite groups by the sum of element orders

Let G be a finite group and \psi(G)=\sum_{g\in G}o(g), where o(g) denotes the order of g\in G. We give a criterion for nilpotency of finite groups G based on the sum of element orders of G. We prove that if \psi(G)>\frac{۱۳}{۲۱}\psi(C_n) then G is a nilpotent group.

کلیدواژه ها:

Finite group‎ ، ‎element orders sum‎ ، ‎nilpotent group‎ ، ‎simple group