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.