Zero Group

The singleton set {0}, with respect to the trivial group structure defined by the addition 0+0=0. The element 0 is the additive identity element of the group, and also the additive inverse of itself.

The zero group is a minimal example of group, hence it is called a trivial group. Another example of trivial group is the multiplicative group {1}, where 1·1=1.

See also

Group, Trivial, Trivial Ring, Zero Ideal, Zero Module, Zero

This entry contributed by Margherita Barile

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Cite this as:

Barile, Margherita. "Zero Group." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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