On the Shemetkov problem for Fitting classes.
Finite groups in which Sylow normalizers have nilpotent Hall supplements.
Conditions for p-supersolubility and p-nilpotency of finite soluble groups
Let ℨ be a complete set of Sylow subgroups of a group G. A subgroup H of G is called ℨ-permutably embedded in G if every Sylow subgroup of H is also a Sylow subgroup of some ℨ-permutable subgroup of G. By using this concept, we obtain some new criteria of p-supersolubility and p-nilpotency of a finite group.
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