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 H = H 0, H 1, H 2, …, H k = G {\displaystyle H=H_{0},H_{1},H_{2},\ldots,H_{k}=G} 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}. Wikipedia