Subnormal subgroup


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, is -subnormal in if there are subgroups
of such that is normal in for each.
A subnormal subgroup is a subgroup that is -subnormal for some positive integer.
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.