Subgroup series

In mathematics, specifically group theory, a subgroup series of a group ${\displaystyle G}$ is a chain of subgroups:

${\displaystyle 1=A_{0}\leq A_{1}\leq \cdots \leq A_{n}=G}$

where ${\displaystyle 1}$ is the trivial subgroup. Subgroup series can simplify the study of a group to the study of simpler subgroups and their relations, and several subgroup series can be invariantly defined and are important invariants of groups. A subgroup series is used in the subgroup method.

Subgroup series are a special example of the use of filtrations in abstract algebra.