International Journal of Mathematics and Mathematical Sciences 
Volume 28 (2001), Issue 8, Pages 455-460
doi:10.1155/S0161171201006457

On a theorem of Schur

Peter Hilton1,2

 1Department of Mathematical Sciences, Suny Binghamton, Binghamton 13902-6000, NY, USA
2Department of Mathematics, University of Central Florida, Orlando 32816-1364, FL, USA
Received 9 January 2001

To the memory of a dear friend and colleague, Paul Olum

Abstract

We study the ramifications of Schur's theorem that, if G is a group such that G/ZG is finite, then G′ is finite, if we restrict attention to nilpotent group. Here ZG is the center of G, and G′ is the commutator subgroup. We use localization methods and obtain relativized versions of the main theorems.