Centralizer and normalizer
= Centralizer and normalizer
{wiki=Centralizer_and_normalizer}
In group theory, which is a branch of abstract algebra, the concepts of centralizer and normalizer help us understand the structure of groups and their subgroups. Here are the definitions of both: \#\#\# Centralizer The centralizer of a subset \\( S \\) of a group \\( G \\), denoted as \\( C_G(S) \\), is the set of all elements in \\( G \\) that commute with every element of \\( S \\).