On finite groups with weakly σ-normal subgroups

Let Formula: see text be a finite group and Formula: see text=Formula: see text some partition of the set of all primes. A subgroup Formula: see text of Formula: see text is said to be Formula: see text Formula: see text-Formula: see text in Formula: see text if there exists a Formula: see text-subnormal subgroup Formula: see text of Formula: see text such that Formula: see text and Formula: see text, where Formula: see text is either Formula: see text-permutably embedded or Formula: see text-semipermutable in Formula: see text. In this paper, we investigate the influence of weakly Formula: see text-normal subgroups on the structure of finite groups.