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, ${\displaystyle H}$ is ${\displaystyle k}$-subnormal in ${\displaystyle G}$ if there are subgroups

of ${\displaystyle G}$ such that ${\displaystyle H_{i}}$ is normal in ${\displaystyle H_{i+1}}$ for each ${\displaystyle i}$.

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