G is Abelian if the Quotient Group G/N is cyclic and N is contained in the Center Proof

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G is Abelian if the Quotient Group G/N is cyclic and N is contained in the Center Proof
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I was really confused about this particular problem...
Thank you so much....:-)

SandeepSharma-ksgb
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What I did was prove that Ng^i is always a subset of Z(G) so their union is also a subset of Z(G) but the union is nothing but G since right cosets partition G and so G is a subset of Z(G) which means G is abelian.

toaj