Group Upper Central Series

The upper central series of a group G is the sequence of groups (each term normal in the term following it)


that is constructed in the following way:

1. Z_1 is the center of G.

2. For n>1, Z_n is the unique subgroup of G such that Z_n/Z_(n-1) is the center of G/Z_(n-1).

If the upper central series of a group terminates with Z_n=G for some n, then G is called a nilpotent group.

See also

Nilpotent Group

This entry contributed by John Renze

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Curtis, C. and Reiner, I. Methods of Representation Theory. New York: Wiley, 1981.

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Group Upper Central Series

Cite this as:

Renze, John. "Group Upper Central Series." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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