Realización de conceptos abstractos de la teoría de grupos por medio de un modelo computacional: estructuras algebraicas.

Abstract

This paper is about the implementation of abstract concepts of group theory by means of a computational model. For its realization, information on group theory and object-oriented programming in the C++ language has been compiled, the main sources of consultation being the Spanish version of Israel Nathan Herstein's Modern Algebra and the fourth edition of the book The C++ Programming. Language by Bjarne Stroustrup. For the development of the component in this paper, the deductive method is used, starting with the most general concepts of algebraic structures such as the definition of group and subgroup; and properties such as being abelian or normal group, to the specification of particular groups that help to visualize said abstract definitions. The paper’s focus is qualitative, based on the description of abstract elements through the collection of information, obtained through a documentary analysis. For the subsequent representation of these abstract concepts through a study of three specific cases using the object-oriented implementation in the C ++ language. The implementation uses the classes tool and the definition of its own objects and the operators and functions that modify them. The main objective of this work is to implement three algebraic groups through a computational model in the C++ language in order to visualize the abstract elements that make up these groups. The result obtained has been the implementation of the Klein, D4 and U8 groups, which allows a better observation of the concepts of group, abelian group, subgroup and normal subgroup. In addition to understanding the operations that define these groups.