Document Type and Release Option
Thesis (restricted to Georgia Southern)
Group theory and its applications are relevant in many areas of mathematics. Our project considers finite groups. More specifically, we are interested in classifying groups of small orders up to isomorphisms. From an algebraic point of view, two isomorphic groups are the same, meaning they have the same properties. For groups of order n, there are n!*n2 possible bijective maps to check for isomorphisms. Thus, checking all possibilities is not an efficient way to classify groups up to isomorphism. For abelian groups, the Fundamental Theorem of Finitely Generated Abelian Groups solves this problem, allowing us to find all classifications of ablelian groups for a given order. For non-abelian groups, the problem becomes much more complicated. We will use results such as Sylow's Theorems to help classify these groups. We will consider various properties that an isomorphism preserves until we have enough evidence to show that two groups are isomorphic.
Yeomans, Katelyn, "Classifying Finite Groups up to Isomorphism" (2014). University Honors Program Theses. 5.