Archiv der Mathematik

, Volume 95, Issue 4, pp 317–318 | Cite as

A generalization of a converse to Schur’s theorem



Niroomand (Arch. Math. 94 (2010) 401–404) proved a converse to a theorem of Schur in the following sense. He proved that if G is a group such that [G, G] is finite and G/Z(G) is finitely generated, then G/Z(G) is finite, of order bounded above by [G, G] k where k is the minimal number of generators required for G/Z(G). Here, we give a completely elementary short proof of a further generalization.

Mathematics Subject Classification (2000)

Primary 20E45 


Commutator subgroup Schur’s theorem 


  1. 1.
    Niroomand P.: The converse of Schur’s theorem. Arch. Math. 94, 401–404 (2010)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  1. 1.Statistics and Mathematics UnitIndian Statistical InstituteBangaloreIndia

Personalised recommendations