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18 - Units of group rings: a short survey

Published online by Cambridge University Press:  07 September 2010

C. Polcino Milies
Affiliation:
University of São Paulo, São Paulo, Brazil
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Summary

INTRODUCTION

Historically group rings appeared for the first time in a paper by A. Cayley which is also considered by many authors as the starting point of abstract group theory (e.g. Bourbaki or M. Kline). They were studied later by T. Molien, and G. Frobenius and earned a definitive status, in connection with group representation theory, after the work of R. Brauer and E. Noether, (regarding the history of group rings see).

In recent times the subject gained impetus after the inclusion of questions on group rings in I. Kaplansky's famous lists of problems. Other important facts to stimulate the area were the inclusion of sections on group rings in the books on ring theory by J. Lambeck and P. Ribemboim as well as the publication of the first book entirely devoted to the subject, due to D.S. Passman.

Since then several survey articles have appeared, namely those by A.E. Zaleskii and A.V. Mikhalev, D.S. Passman, K. Dennis and D. Farkas. Also new books on the subject have been published in recent years: A.A. Bovdi, I.B.S. Passi, D.S. Passman and S.K. Sehgal.

Considerable work has been done lately on the structure and group-theoretical properties of the group of units of a group ring.

Type
Chapter
Information
Groups - St Andrews 1981 , pp. 281 - 297
Publisher: Cambridge University Press
Print publication year: 1982

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