Trabajo Fin de Grado
Clasificación de grupos cristalográficos planos
Autor/es | Coba Carpio, Pilar |
Director | Aguilera Gómez del Castillo, Marta
González-Meneses López, Juan ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Departamento | Universidad de Sevilla. Departamento de Álgebra |
Fecha de publicación | 2022-06-15 |
Fecha de depósito | 2022-06-15 |
Titulación | Universidad de Sevilla. Grado en Matemáticas |
Resumen | Crystallographic groups are groups whose elements are isometries of a metric space. These groups are 17 in the
Euclidean plane and we can find them in nature or tilings. Many scientists study these groups in fields ... Crystallographic groups are groups whose elements are isometries of a metric space. These groups are 17 in the Euclidean plane and we can find them in nature or tilings. Many scientists study these groups in fields other than Mathematics, such as Chemistry. Throughout history, some people have given the list of 17 groups, and have been interested in the study of them in higher dimensions. In this work there are two different blocks. In the first one, we recall some concepts of group theory. Then we explain how a group acts on the elements of a set. Finally we recall some notions of Euclidean plane to explain the isometries of the plane. The second part of this work focuses on an article of Schwarzenberger [14]. We show what is a crystallographic group and we prove that there are exactly 17 of them. To do that, we divide the groups into three types: those which contain, respectively, no reflections, exactly one or more than one. In addition, we have included pictures for an easier understanding of the text, and examples of each group. |
Cita | Coba Carpio, P. (2022). Clasificación de grupos cristalográficos planos. (Trabajo Fin de Grado Inédito). Universidad de Sevilla, Sevilla. |
Ficheros | Tamaño | Formato | Ver | Descripción |
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Coba Carpio Pilar TFG.pdf | 2.967Mb | ![]() | Ver/ | |