In mathematics, specifically group theory, a subgroup series of a group G {\displaystyle G} is a chain of subgroups: 1 = A 0 ≤ A 1 ≤ ⋯ ≤ A n = G {\displaystyle 1=A_{0}\leq A_{1}\leq \cdots \leq A_{n}=G} where 1 {\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.
In mathematics, specifically group theory, a subgroup series of a group G {\displaystyle G} is a chain of subgroups: 1 = A 0 ≤ A 1 ≤ ⋯ ≤ A n = G {\displaystyle 1=A_{0}\leq A_{1}\leq \cdots \leq A_{n}=G} where 1 {\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.
Source: Wikipedia "Subgroup series" · CC BY-SA 4.0
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