On the converse of a theorem of Schur
A well known theorem of Schur states that for any group G, if G/Z(G) is finite, then G′ is finite. We give a very short and elementary proof of a further generalization of the converse of Schur’s theorem proved by Niroomand  and Sury  and also improve the bound for the order of G/Z(G) obtained by Niroomand and Sury.
Mathematics Subject Classification (2010)20D45 20D15
KeywordsSchur’s theorem Nilpotent group
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- 8.M. K. Yadav, Converse of Schur’s theorem—a statement, available at http://arxiv.org/pdf/1212.2710.pdf