ABSTRACT
This section defines the abstract notion of group, after examining two important examples: symmetries of regular n-sided polygons (called the nth dihedral groups) and symmetries of the regular tetrahedron and the cube in 3-space. A group G is a set of elements with one binary operation (◦) that
satisfies three rules:
1. (g ◦ h) ◦ k = g ◦ (h ◦ k), for all g, h, k ∈ G, 2. There exists an element e ∈ G (called the identity of G) such that g ◦ e = e ◦ g = g for all g ∈ G, and
3. For each g ∈ G, there exists an element x (called the inverse of g) such that g ◦ x = x ◦ g = e.
