What group is not abelian?
Could you please elaborate on the concept of an abelian group and then provide an example of a group that does not possess the properties that define an abelian group? I'm particularly interested in understanding the key characteristics that distinguish an abelian group from a non-abelian group, and how this distinction affects their mathematical properties and applications.
What is the smallest non-Abelian group?
Could you please elaborate on what the smallest non-Abelian group is? I'm curious to understand the properties and characteristics that make it unique from Abelian groups. Additionally, how does it differ in structure and operation from larger non-Abelian groups? It would be helpful if you could provide an example to illustrate your explanation.