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  3. let g be a group. the center of, denoted by z(g),

Let G be a Group. The center of, denoted by Z(G), is defined to be the...

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Advance Math

Let G be a Group. The center of, denoted by Z(G), is defined tobe the set of all elements of G that with every element of G.Symbolically, we have

Z(G) = {x in G | ax=xa for all a in G}.

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

(b) Prove that Z(G) is an Abelian group.

Answer & Explanation Solved by verified expert
4.2 Ratings (540 Votes)
GivenThe center of denoted by ZG is defined to be the set of allelements of G that with every element of G Symbolicallywe    See Answer
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