Solubility of finite groups

Let H be a p-subgroup of G. Then: ① H satisfies Φ*-property in G if H is a Sylow subgroup of some subnormal subgroup of G and for any non-solubly-Frattini chief factor L/K of G, |G:NG(K(H∩L))| is a power of p; ② H is called Φ*-embedded in G if there exists a subnormal subgroup T of G such that HT is S-quasinormal in G and H∩T≤S, where S≤H satisfies Φ*-property in G. Here Φ*-embedded subgroups were used to study the structure of finite groups and, in particular, some new characterizations for a group G to be soluble are obtained.