In mathematics, in the field of group theory, a subgroup H of a given group G is a subnormal subgroup of G if there is a finite chain of subgroups of the group, each one normal in the next, beginning at H and ending at G. In notation, H is k-subnormal in G if there are subgroups of G such that H_i is normal in H_{i+1} for each i. A subnormal subgroup is a subgroup that is k-subnormal for some positive integer k. Some facts about subnormal subgroups: The property of subnormality is transitive, that is, a subnormal subgroup of a subnormal subgroup is subnormal. The relation of subnormality can be defined as the transitive closure of the relation of normality. If every subnormal subgroup of G is normal in G, then G is called a T-group.