Mortorff, Maleah, "William Burnside: Theory of Groups of Finite Order and the Burnside Problem" (2016). Senior Honors Theses. 566.
As one of the most influential founders of modern group theory, William Burnside and his work generated initial interest in the field of group theory. His book Theory of Groups of Finite Order was regarded for several decades as the standard measure for group research. Namely, the General Burnside Problem examines a finitely generated periodic group, questioning whether or not that group must be necessarily finite. Breakdowns in this general problem led to a definitive negative answer by Evgeny Golod and Tgor Shararevich in 1964, but paved the way for research into specific cases such as the prime exponent. This thesis will consider the background of Burnside’s mathematical expertise, as well as the general, bounded, and restricted cases of Burnside’s problem, concluding with a brief overview of his theorem and lemma.