Subnormal subgroup

Subnormal subgroup: A subgroup of a group such that there is an ascending chain of subgroups, starting from that subgroup to the whole group, with each member normal in the next. Such an ascending chain is termed a subnormal series.

A $$k$$-subnormal subgroup is a subgroup for which there exists a subnormal series of length at most $$k$$. Particular examples are $$k = 1$$ (normal subgroup), $$k = 2$$ (2-subnormal subgroup), $$k = 3$$ (3-subnormal subgroup).

Primary subject wiki entry: Groupprops:Subnormal subgroup

Related terms: Normal subgroup, 2-subnormal subgroup, 3-subnormal subgroup, ascendant subgroup, descendant subgroup, serial subgroup, subnormal series, normal series