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edited Jul 18, 2011 at 15:41

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If H is a subgroup of Z(G) and G/H is nilpotent, then G is nilpotent.

Can you help me and give me the proof of this statement please? And can you explain me why this statement is not true when $H$ is not a subgroup of $Z(G)$? Thank you very much

gr.group-theory

asked Jul 18, 2011 at 15:23

Roberto