Date of Award
Bachelor of Science
groups, order, thesis, classifying, group
This thesis will provide an overview of various topics in group theory, all in order to accomplish the end goal of classifying all groups of order up to 15. An important precursor to classifying ﬁnite order groups, the Sylow Theorems illustrate what subgroups of a given group must exist, and constitute the ﬁrst half of this thesis. Using these theorems in the latter sections we will classify all the possible groups of various orders up to isomorphism. In concluding this thesis, all possible distinct groups of orders up to 15 will be deﬁned and the groundwork set for further study.
Stearns, William, "The Sylow Theorems and Classification of Small Finite Order Groups" (2015). Honors Theses and Student Projects. 395.