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