Based on Wielandt's criterion for subnormality of subgroups in finite groups,we study 2-maximal subgroups of finite groups and present another subnormality criterion in finite solvable groups.
A subgroup H of a finite group G is called a c*-normal subgroup of G if there exists a normal subgroup K of G such that G = HK and H ∩ K is an S-quasinormal embedded subgroup of G. In this paper, the structure of a finite group G with some c*-normal maximal subgroups of Sylow subgroups is characterized and some known related results are generalized.
