Source: wikibot/central-subgroup
= Central subgroup
{wiki=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.