Let G be a finite group and M a maximal subgroup of G. A theta-completion of M in G is any subgroup C such that C is not contained in M while M-G, the core of M in G, is contained in G and C/M-G has no proper normal subgroup of G/M-G. The concept of theta -completion offers a convenience for us to study the Deskins completions. By using this concept and in a quite different way from what was used, we obtain some new results about the maximal completions and theta-completions which imply G to be solvable and supersolvable. [References: 12]
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