University of Isfahan International Journal of Group Theory 2251-7650 12 1 2023 03 01 New criteria for solvability, nilpotency and other properties of finite groups in terms of the order elements or subgroups 35 44 26287 10.22108/ijgt.2022.131888.1766 EN Marcel Herzog Dipartimento di Matematica, Università di Salerno, via Giovanni Paolo II, 132, 84084 Fisciano (Salerno), Italy Patrizia Longobardi Dipartimento di Matematica, Università di Salerno, via Giovanni Paolo II, 132, 84084 Fisciano (Salerno), Italy Mercede Maj Dipartimento di Matematica, Università di Salerno, via Giovanni Paolo II, 132, 84084 Fisciano (Salerno), Italy Journal Article 2021 12 15 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 $G$. element orders solvability nilpotency https://ijgt.ui.ac.ir/article_26287_b289df06ad4eb960eea5c16bde5aa245.pdf