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# On Zero-divisors in Group Rings of Groups with Torsion

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Published:2012-12-29
Printed: Jun 2014
• S. V. Ivanov,
Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, IL 61801, USA
• Roman Mikhailov,
Steklov Mathematical Institute, Gubkina 8, Moscow, 119991, Russia
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## Abstract

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: Burnside groups, free products of groups, group rings, zero-divisors
 MSC Classifications: 20C07 - Group rings of infinite groups and their modules [See also 16S34] 20E06 - Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations 20F05 - Generators, relations, and presentations 20F50 - Periodic groups; locally finite groups

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