Burnside's $p^{a} q^{b}$ theorem

Abstract

[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.