##  [Lower Central Series](/lower-central-series) 

  ##  [Lower Central Series](https://algebra.quantumdictionary.io/lower-central-series-0) 

  

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- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The descending sequence of subgroups defined by γ_1(G) = G and γ_{n+1}(G) = [G, γ_n(G)], where each term is the subgroup generated by commutators of the whole group with the previous term; it measures nilpotency by progressively forcing successive commutator layers to vanish.