Zarzuela, SantiagoSantiago Blanco, Víctor2023-04-142023-04-142022-06-12https://hdl.handle.net/2445/196781Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2022, Director: Santiago Zarzuela[en] The main goal of this work is to prove the Burnside’s $p^{a} q^{b} -theorem, which states that every group $G$ of order $p^{a} q^{b}$ is solvable. In order to justify the importance of this well-known theorem, a first chapter about solvable groups will be included, in which will be analyzed some properties of solvable groups. The provided proof will use Representation and Character Theory which will be studied in depth.63 p.application/pdfengcc-by-nc-nd (c) Víctor Santiago Blanco, 2022http://creativecommons.org/licenses/by-nc-nd/3.0/es/Representacions de grupsTreballs de fi de grauAnells de grupTeoria de grupsRepresentations of groupsBachelor's thesesGroup ringsGroup theoryinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess