MHB Lower Central Series: Meaning of Gamma of G

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The notation gamma of G, represented as γ_n(G), refers to the n-th term of the lower central series of a group G. It serves as a descriptive notation similar to sequences in mathematics, where each term is defined by a specific operation. The lower central series is unique to each group, allowing the gamma notation to act as an operator that maps the group to its corresponding term in the series. This notation helps in understanding the structure and properties of the group through its lower central series. Overall, gamma of G is a crucial concept in group theory for analyzing group behavior.
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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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