Define center ,nomalizer........?

3.If G is a group and H is a subgroup of G and A is tha subset of G the Define :


1.C(G)(A)


2.NG (H)


3.If A=G then Ng(H) and CG(A).

Define center ,nomalizer........?
C_G(A) is called the centralizer of A in G and is the set of all elements in G that commute with all elements of A.





C_G(A)= { x in G | xa=ax for any a in A}





N_G(H) = { x in G | x H x^(-1) = H }





If A=G then C_G(G) = The center of group G





If A=G then N_G(G) = G