## ABSTRACT

We have already seen some patterns within a group, such as the Latin square property. However, in order to determine more patterns, we need to consider the possibility of a smaller group sitting inside of a larger group. For example, the group of integers is inside of the group of real numbers. Whenever this happens, we say the smaller group is a subgroup of the larger group. Subgroups will lead to even more important properties of groups. But before we determine the subgroups of a given group, we need to understand the generators of a group.