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On Zero-divisors in Group Rings of Groups with Torsion |
8 pages
Published:2012-12-29
- S. V. Ivanov,
- Roman Mikhailov,
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 |