non-Abelian
Adjective
Meaning
non-Abelian (not comparable)
Alternative form of nonabelian.
Examples
A group in which the group operation is not commutative is called a "non-abelian group" or "non-commutative group".
A similar unsolved (as of 2011) question in free probability theory asks whether the von Neumann group algebras of any two non-abelian finitely generated free groups are isomorphic.
Since the Galois group of the general quintic equation is isomorphic to the symmetric group on five letters, and this normal subgroup is simple and non-abelian, the general quintic equation does not have a solution in radicals.
For general non-abelian locally compact groups, harmonic analysis is closely related to the theory of unitary group representations.
For a non-abelian example, consider the subgroup of rotations of R 3 generated by two rotations by irrational multiples of 2π about different axes.
For this behaviour the non-abelian behaviour of the gauge group is essential.