ON THE DESKINS COMPLETIONS, THETA-COMPLETIONS AND THETA-PAIRS FOR MAXIMAL-SUBGROUPS-II

This paper is a continuation of the paper ''On the Deskins completions , theta completions and theta pairs for maximal subgroups''. In the fo rmer paper, Zhao Yaoqing introduced the concept of theta-completions a ssociated to a maximal subgroup of a finite group. The concept offers a convenience for us to study the completions introduced by Deskins an d gives us a way to reveal the relationship between the concepts of co mpletions and theta-pairs, the latter concept is introduced by Mukherj ee and Bhattacharya. The present paper is devoted to discussing the pi -solvability, pi-supersolvability and pi-nilpotency of a finite group by using the theta-completions. Moreover, a new proof on the Deskins c onjecture concerning the supersolvability is included.