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On Zero-divisors in Group Rings of Groups with Torsion

Published online by Cambridge University Press:  20 November 2018

S. V. Ivanov  and
Roman Mikhailov
S. V. Ivanov
Affiliation:
Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, IL 61801, USA e-mail: ivanov@math.uiuc.edu
Roman Mikhailov
Affiliation:
Steklov Mathematical Institute, Gubkina 8, Moscow, 119991, Russia e-mail: romanvm@mi.ras.ru Chebyshev Laboratory, St. Petersburg State University, 14th Line, 29b, Saint Petersburg, 199178 Russia
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Abstract

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Nontrivial pairs of zero-divisors in group rings are introduced and discussed. A problem on the existence of nontrivial pairs of zero-divisors in group rings of free Burnside groups of odd exponent $n\,\gg \,1$ is solved in the affirmative. Nontrivial pairs of zero-divisors are also found in group rings of free products of groups with torsion.

Keywords

20C0720E0620F0520F50Burnside groupsfree products of groupsgroup ringszero-divisors
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 57 , Issue 2 , 14 June 2014 , pp. 326 - 334
Copyright
Copyright © Canadian Mathematical Society 2014

Footnotes

The first author is supported in part by NSF grant DMS 09-01782. This research of the second author is supported by the Chebyshev Laboratory (Department of Mathematics and Mechanics, St. Petersburg State University) under RF Government grant 11.G34.31.0026

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