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Lower Central Series

The lower central series of a group G is the descending sequence of subgroups

gamma_1(G)=G, gamma_(n+1)(G)=[G,gamma_n(G)],

where [G,H] denotes the subgroup generated by the commutators [g,h] with g in G and h in H. The group G is nilpotent precisely when gamma_(c+1)(G) is the trivial group for some c; the least such c is its nilpotency class.

See also

Commutator Subgroup, Group Upper Central Series, Lie Algebra Lower Central Series, Nilpotent Group

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References

Hall, M., Jr. The Theory of Groups. New York: Macmillan, 1959.

Cite this as:

Weisstein, Eric W. "Lower Central Series." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LowerCentralSeries.html

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