New criteria for solvability, nilpotency and other properties of finite groups in terms of the order elements or subgroups

Abstract

In this survey we shall describe some recent criteria for solvability, nilpotency and other properties of finite groups $G$, based either on the orders of the elements of $G$ or on the orders of the subgroups of $G$.

Keywords

• element orders
• solvability
• nilpotency