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On Zero-divisors in Group Rings of Groups with Torsion

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