Question

If a group is not abelian, what do you understand? There exists a normal subgroup for the group. Provide an example.

Answer 1

In mathematics, an abelian group is a group where the order of the elements does not matter. If a group is not abelian, it means that there exists at least one pair of elements for which the group operation is not commutative. An example of a non-abelian group is the group of square matrices of size 2x2 with real entries.

Step-by-step explanation:

In mathematics, an abelian group or commutative group is a group where the order of the elements does not matter.

In other words, the group operation is commutative, meaning that for any two elements of the group, the result of applying the operation is the same regardless of the order in which the elements are combined.

If a group is not abelian, it means that there exists at least one pair of elements for which the group operation is not commutative.