Spectra of Semidirect Products of Cyclic Groups
نویسنده
چکیده
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, eld theory, and representation theory. The main result of this paper gives a formula that can be used to nd the spectrum of semidirect products of cyclic groups. Acknowledgements: This reasearch was carried out at Canisius College with funding from the National Science Foundation. The author would like to thank Dr. Terrence Bisson for his assistance. Page 132 RHIT Undergrad. Math. J., Vol. 11, No. 2
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تاریخ انتشار 2010