What is the opposite of abelian?
Excuse me, could you please elaborate on the concept of "abelian" and then guide me towards understanding its opposite? I'm familiar with abelian groups in mathematics, but I'm curious to know if there's a specific term or concept that describes the properties or structures that are not abelian in nature. Additionally, I'm interested in knowing how these non-abelian structures differ from abelian ones and what implications they may have in various fields, particularly in cryptography and finance where the properties of mathematical groups play a significant role.