**Definition 5**. A **group** \(G\) is a monoid in which all \(a \in G\) have an
**inverse** element \(b \in G\) with \(a \circ b = b \circ a = e\). A group \(G\) is an **Abelian
group** if it is a commutative monoid.

**Definition 5**. A **group** \(G\) is a monoid in which all \(a \in G\) have an
**inverse** element \(b \in G\) with \(a \circ b = b \circ a = e\). A group \(G\) is an **Abelian
group** if it is a commutative monoid.