Non-abelian group, in mathematics, a group that is not abelian (commutative)
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See the books by Irving Kaplansky, László Fuchs, Phillip Griffith, and David Arnold, as well as the proceedings of the conferences on Abelian Group Theory published in Lecture Notes in Mathematics for more recent results.
Based on these properties, the class of combinatorial games may be thought of as having the structure of an Abelian group, although with a proper class of elements rather than (as is more standard for groups) a set of elements.
Mathematically, a Yang–Mills instanton is a self-dual or anti-self-dual connection in a principal bundle over a four-dimensional Riemannian manifold that plays the role of physical space-time in non-abelian gauge theory.
The link group of the Hopf link, the simplest non-trivial link – two circles, linked once – is the free abelian group on two generators, Note that the link group of two unlinked circles is the free nonabelian group on two generators, of which the free abelian group on two generators is a quotient.