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! :-)

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- Dec 16th 2008, 07:28 AMPolyxendiAbtract 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! :-) - Dec 16th 2008, 07:37 AMIsomorphism