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Jun 1, 2012 at 17:02 vote accept Todd Leason
May 26, 2012 at 18:40 comment added Jim Humphreys @Geoff: Thanks for the wider perspective on this area of research. I was commenting more narrowly just on the positive solution of the isomorphism problem for group rings given for certain groups by Roggenkamp and Scott (though their work goes farther than this problem).
May 26, 2012 at 5:36 comment added Geoff Robinson Roughly speaking (for one possible direction of application) It is sometimes possible to show the existence of central units in integral or modular group rings which, if they could be shown to be genuine group elements, would give a proof of some interesting general group-theoretic conjectures.
May 26, 2012 at 0:07 comment added Jim Humphreys My recollection (not precise) is that S.K. Sehgal wrote an older book, which is probably outdated in many directions, but also co-authored a more recent textbook which includes much of the work on group rings and related matters.
May 25, 2012 at 23:00 comment added Todd Leason Thanks for your answer. Do you know the title of the book on the isomorphism problem you mentioned ?
May 25, 2012 at 22:29 history answered Jim Humphreys CC BY-SA 3.0