Show these are subgroups of a group G?

[Firepanda]

Z(G) = { x in G : xg=gx for all g in G } (center of a group G)

and

C(g) = { x in G : xg=gx } (centralizer of g in G)Z(G) is a subgroup by the proof here:

http://en.wikipedia.org/wiki/Center_(group_theory)#As_a_subgroupHow do I go about showing C(g) is a subgroup? The proofs look like they should be identical to me, but then why do I have 2 separate questions for it?

Thanks

 

[Dick]

They are two different questions because Z(G) is not the same thing as C(g). Yes, the proofs are almost identical. So just go ahead and prove C(g) is a group.