non-abelian groups
A non-abelian group is a type of mathematical group where the order of operations matters. In other words, if you take two elements from the group and combine them, changing the order of those elements will yield a different result. This property distinguishes non-abelian groups from abelian groups, where the order does not affect the outcome.
An example of a non-abelian group is the group of rotations of a cube. When you rotate the cube in one direction and then in another, the final position depends on the order of those rotations. This complexity makes non-abelian groups important in various fields, including group theory and physics.