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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, H {\displaystyle H} is k {\displaystyle k} -subnormal in G {\displaystyle G} if there are subgroups
of G {\displaystyle G} such that H i {\displaystyle H_{i}} is normal in H i + 1 {\displaystyle H_{i+1}} for each i {\displaystyle i}.
A subnormal subgroup is a subgroup that is k {\displaystyle k} -subnormal for some positive integer k {\displaystyle k}.Some facts about subnormal subgroups: