The Deskins Maximal Completions And Complemented Subgroups Of Finite Groups

In this paper, considering some special maximal subgroups of a given group G, the solvability or the supersolvability of G is discussed under weaker conditions by using the properties of maximal completions of finite groups. Especially, we introduce M₁(G) and M₂(G), two sets of maximal subgroups of G and get a series of results. In addition, we characterize the structure of a group G through considering its some complemented subgroups' exisence and generalize two theorems, which are proved in [1] and [2] , to a formation.