Abstract: Let F be a saturated formation of finite groups. Given a proper subgroup H of a group G, a subgroup H of G is called F-normal in G if G/HGbelongs to F; otherwise H is said to be F-abnormal in G. In this paper, we investigate the structure of a finite group by θ*completions of F-abnormal subgroups. 

Key words: θ*-completions, maximal subgroups, 2-maximal subgroups, F-abnormal subgroups