# An Introduction to Commutative Trinary Groups

This paper is an introduction to the notion of a trinary group: a set with a trinary operation. The paper was hastily written for my UROP over the summer of 2010 to put together some of their properties so that I could perhaps use the ideas for my research (see Classification of quadratic iteration graphs).

In this document, we will define the notion of a commutative
trinary group, which is group-like algebraic object with an
associated trinary operation, show basic properties of these
objects, and determine the trinary subgroups of **F**_{p}^{*} useful
for understanding the basic structure of quadratic residue
graphs. We will only talk about trinary groups which are
commutative 1) because of the difficulties inherent in
non-commutative algebra and 2) because the motivation in studying
trinary groups is to understand quadratic residues in **F**_{p}^{*}.

Download the paper: (PDF)