By the center of a group G we mean the set of all the elements of G which commute with every element of G, that is,
C = {a e G : ax = xa for every x e G}
Prove that C is a subgroup of G.
Any advice? I have no idea how to do this...
By the center of a group G we mean the set of all the elements of G which commute with every element of G, that is,
C = {a e G : ax = xa for every x e G}
Prove that C is a subgroup of G.
Any advice? I have no idea how to do this...
When proving a given set, , is a subgroup there are two things you need to prove,
Given then,
, and
.
So, let and , the center of .
Does ? Yes, it does, but show it.
Does ? Yes, it does. However, there is a `trick' to this one. You need to remember that if then , and that as .