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Non-Abelian

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A non-Abelian group or other algebraic object is one for which the law of commutativity does not always hold, i.e., the object is not Abelian. For example, the group of 2×2 nonsingular matrices with real entries is non-Abelian, as can be seen by comparing

[1 0; 0 -1][0 1; -1 0]=[0 1; 1 0]

and

[0 1; -1 0][1 0; 0 -1]=[0 -1; -1 0].

See also

Abelian, Abelianization, Group, Non-Abelian Group, Ring

This entry contributed by Todd Rowland

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Cite this as:

Weisstein, Eric W., with contributions by Todd Rowland. "Non-Abelian." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Non-Abelian.html

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