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In mathematics, specifically group theory, a subgroup series of a group G {\displaystyle G} is a chain of subgroups:
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. A subgroup series is used in the subgroup method.
Subgroup series are a special example of the use of filtrations in abstract algebra.
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