On sigma-subnormal closure

摘要

Let be a partition of the set of all prime numbers. A subgroup A of a finite group G is called sigma-subnormal in G if there is a chain of subgroups with normal in A(i) or is a -group for some for every In this paper, the description of the unique smallest sigma-subnormal subgroup of a sigma-soluble group containing a given subgroup is obtained.