Title

Groups of Graphs of Groups

Document Type

Thesis

Publication Date

2011

Advisor

Thomas Sibley, Mathematics

Abstract

We can construct an edge colored complete graph of a group by generalizing the notion of distance in the reals. Each graph of a group has color preserving bijections called isometries, and the collection of all isometries of a group forms a new group. We have classified the isometry groups of all groups, and I will discuss in detail my part of this classification. I will discuss the use of direct products and semi-direct products for discovering isometry groups, and I will show that abelian groups and dicyclic groups are the building blocks for groups whose isometry group is twice as big as the original group.

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