
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, formula_1 is formula_2-subnormal in formula_3 if there are subgroups
of formula_3 such that formula_6 is normal in formula_7 for each formula_8.
A subnormal subgroup is a subgroup that is formula_2-subnormal for some positive integer formula_2.
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.