Central subgroup

In group theory, a branch of abstract algebra, a **central subgroup** refers to a subgroup that is contained in the center of a given group. The center of a group \( G \), denoted \( Z(G) \), is defined as the set of all elements \( z \in G \) such that \( zg = gz \) for all \( g \in G \). In other words, the center consists of all elements that commute with every other element in the group.