Subnormal subgroup

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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. In fact, the relation of subnormality can be defined as the transitive closure of the relation of normality.

See also

References

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