Archiv der Mathematik

, Volume 101, Issue 1, pp 17–20 | Cite as

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 [5] and Sury [7] and also improve the bound for the order of G/Z(G) obtained by Niroomand and Sury.

Mathematics Subject Classification (2010)

20D45 20D15 


Schur’s theorem Nilpotent group 


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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.School of Mathematics and Computer ApplicationsThapar UniversityPatialaIndia

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