Thread: Abtract algebra help!

For any group G, the set of all the elements that commute with every element of G is called the center of G and it's denoted by:

Z(G) = {a ∈ G, such that ax = xa, ∀ x ∈ G}

Prove that Z(G) is a subset of G.


Any ideas?

Thanks! :-)

Originally Posted by Polyxendi

For any group G, the set of all the elements that commute with every element of G is called the center of G and it's denoted by:

Z(G) = {a ∈ G, such that ax = xa, ∀ x ∈ G}

Prove that Z(G) is a subset of G.


Any ideas?

Thanks! :-)

I think you mean:
"Prove that Z(G) is a subgroup of G"

In that case,