1. Some sufficient and necessary conditions for -supersolvablity and -nilpotence of a finite group. Author Yu, Haoran Subjects *FINITE groups, *GENERALIZATION, *MATHEMATICAL analysis, *FC-groups, *MATHEMATICS Abstract In this paper, we generalize the main results of Guo and Isaacs, Archiv der Mathematik 105 (2015) 215-222. We also obtain some criteria for -nilpotency of a finite group. [ABSTRACT FROM AUTHOR] Published 2017 Full Text View/download PDF