Why is the Klein 4 group not cyclic?
Can you explain to me, in simple terms, why the Klein 4 group, also known as the Vierergruppe or the group of order 4, is not considered cyclic? I understand that a cyclic group is one in which the elements are arranged in a way that every non-identity element can be expressed as a power of a single element, known as the generator. So, what specific property or characteristic of the Klein 4 group prevents it from being cyclic?