| Center |
| Faculty of Mathematics |
| Departament |
| Algebra |
| Lecturers in charge |
| Sin datos cargados |
| Met. Docent |
| In the theoretical sessions, the active part of its development corresponds basically to the professor. One will harness the participation and the work in the classroom of the students, particularly in the practical exercises. |
| Met. Avaluació |
| A theoretical-practical examination will be made. In the final qualification the resolution of questions will be able also be valued, problems and the exhibition of subjects that possibly can consider. |
| Bibliografia |
| Doerk, K., T.O. Hawkes, “Finite soluble groups”, Walter de Gruyter, 1992. Isaacs, I. M., “Algebra”, Brooks/Cole Publishing Company, 1994. Kurzweil, H., Stellmacher, B., “The Theory of Finite Groups. An Introduction”, Springer-Verlag, 2004. Robinson, D.J.S., “A course in the theory of groups”, Springer-Verlag, 1980. Rose, J. S., “A course on group theory”, Cambridge University Press, 1978. |
| Continguts |
| As much if the study of group theory has like object its application to other areas as if a researchin this theory is tried, it is necessary the knowledge of free groups,generators and relations,and presentations of groups. The concept of action is implicit in the nature of the groups, initially with permutation groups but also like transformations or actions on objects and structures of diverse nature. It is thus necessary the study of group actions on groups and its first application to the construction of the semidirect product. The theorem of Schur-Zassenhaus like basic result on decompositions of groups will also be approached. The concept of solubility appears already in the origin of group theory, related to the resolution of algebraic equations by means of radicals, and continues being key in all its development. Its influence affects so much to the arithmetic aspect of its study like to the one of its normal structure. It interests therefore the study of soluble groups, in particular of determined orders, constituting the paqb-theorem of Burnside a reference result. In this context of solubility it also appears the extension of Sylow and p-groups theories, in particular through the Hall theory. The knowledge of the students acquired in other areas will be applied, in particular linear and multilinear algebra and geometry, to the study of groups. Some applications of group theory will be illustrated. |
| Objetius |
| To reach a level of knowledge in group theory that enables students as much to approach subjects and questions in which this theory plays an important role (symmetries and groups of transformations, crystallographic groups, graph theory, computer sciences, etc.) like continuing with an own research in this discipline. |
| URL de Fitxa |