A group or other algebraic object is called non-Abelian if the law of commutativity does not always hold, i.e., if the object is not Abelian. For example, the group of nonsingular matrices is non-Abelian, as can be seen by comparing
![[1 0; 0 -1][0 1; -1 0]=[0 1; 1 0]](/images/equations/Non-Abelian/NumberedEquation1.svg) |
and
![[0 1; -1 0][1 0; 0 -1]=[0 -1; -1 0].](/images/equations/Non-Abelian/NumberedEquation2.svg) |
Non-Abelian
See also
Abelian, Abelianization, Group, Non-Abelian Group, RingThis entry contributed by Todd Rowland
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Rowland, Todd. "Non-Abelian." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/Non-Abelian.html