| The theory of groups seeks to be the foundation of mathematics. All mathematical constructions are defined and obtained starting from the primitive notions of group and ownership. Those primitive notions are subject to fulfilling a series of axioms that capture the principles of "true groups". Our objective is to develop the theory of groups of Zermelo-Fraenkel-Skolem axiomatically. In order to do so, we will compare groups that do not possess any additional structure, by means of applications, reaching comparisons that will lead us to the concept of cardinal numbers and cardinal arithmetic. Another concept to be studied is that of groups that follow some kind of order, using morphological applications that preserve the structures involved, comparison that will lead us, to the concept o |
