International Journal of Mathematics and Mathematical Sciences
Volume 28 (2001), Issue 8, Pages 455-460
doi:10.1155/S0161171201006457
On a theorem of Schur
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
Copyright © 2001 Peter Hilton. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.