On zero-divisors in group rings of groups with torsion

S. V. Ivanov^a, R. Mikhailov<sup>bc

a</sup> Department of Mathematics, University of Illinois at Urbana-Champaign
^b Steklov Mathematical Institute, Gubkina 8, Moscow, 119991, Russia
^c Chebyshev Laboratory, St. Petersburg State University, Department of Mathematics and Mechanics

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 is solved in the affirmative. Nontrivial pairs of zero-divisors are also found in group rings of free products of groups with torsion.

MSC: Primary 20C07; Secondary 20E06, 20F05, 20F50

Language: English

DOI: 10.4153/CMB-2012-036-6

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