(adsbygoogle = window.adsbygoogle || []).push({}); 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_subgroup

How 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 seperate questions for it?

Thanks

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# Homework Help: Show these are subgroups of a group G?

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