ABSTRACT
A nonempty set H together with a binary operation ♦: H × H ⎯→ H is a group if the following three conditions are satised:
1. For all elements a, b, c ∈ H, we have a♦(b♦c) = (a♦b)♦c.
2. There exists an element e ∈ H such that for each element x ∈ H, x♦e = e♦x = x.