# Changes

* A group $G$ is termed abelian if its it satisfies the following equivalent conditions: * Its [[defining ingredient::center]] $Z(G)$ is the whole group.* A group is abelian if its Its [[defining ingredient::derived subgroup]] $G" = [G,G]$ is trivial.* (Choose a generating set $S$ for $G$). For any elements $a,b \in S$, $ab = ba$.