## Abstract

The spectrum of a graph is the set of eigenvalues of its adjacency matrix. A group, together with a multiset of elements of the group, gives a Cayley graph, and a semidirect product provides a method of producing new groups. This paper compares the spectra of cyclic groups to those of their semidirect products, when the products exist. It was found that many of the interesting identities that result can be described through number theory, field theory, and representation theory. The main result of this paper gives a formula that can be used to find the spectrum of semidirect products of cyclic groups.

## Faculty Sponsor

Terrence Bisson

## Recommended Citation

Fox, Nathan
(2010)
"Spectra of Semidirect Products of Cyclic Groups,"
*Rose-Hulman Undergraduate Mathematics Journal*: Vol. 11:
Iss.
2, Article 7.

Available at:
https://scholar.rose-hulman.edu/rhumj/vol11/iss2/7