Lower Central Series: Meaning of Gamma of G

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SUMMARY

The discussion clarifies the meaning of the notation $\gamma_{n}(G)$ in the context of the lower central series of a group. Specifically, $\gamma_{n}(G)$ represents the $n$-th term of the lower central series, denoted as $G_{n}$. This notation functions as an operator that maps a group to its corresponding term in the series, emphasizing the uniqueness of the lower central series for any given group.

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  • Understanding of group theory concepts, particularly central series.
  • Familiarity with mathematical notation and operators.
  • Knowledge of the properties of lower central series in algebra.
  • Basic comprehension of sequences in mathematics.
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Mathematicians, particularly those specializing in group theory, algebraists, and students seeking to deepen their understanding of central series and their applications in various mathematical contexts.

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In definition of lower central series we use the notation called ,gamma of G, what is meaning of this gamma of G ? please help...
 
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Hi,

Do you refer the notation in wiki?
Central series - Wikipedia, the free encyclopedia

There, $\gamma_{n}(G)=G_{n}$ it's just a description notation, I mean, this is like when you take a sequence and write $a_{n}=(whatever)$ but in this case, as the lower central series of a group is unique we can think in an "operator" family ($\gamma_{n}$) that sends every group to the $n-$th term of his lower central series ($G_{n}$).
 

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