# A remark on group rings of periodic groups

Document Type : Research Paper

Author

Assitant at Armenian-Russian State University

Abstract

A positive solution of the problem of the existence of nontrivial pairs of zero-divisors in group rings of free Burnside groups of sufficiently large odd periods $n>10^{10}$ obtained previously by S‎. ‎V‎. ‎Ivanov and R‎. ‎Mikhailov extended to all odd periods $n\geq665$‎.

Keywords

Main Subjects

#### References

[1] Kourovka Notebook. Unsolved problems in group theory, 18th edition, (2014), Edited by V. D. Mazurov and E. I. Khukhro. Inst. Mat., Novosibirsk.

[2] S. V. Ivanov and R. Mikhailov, On zero-divisors in group rings of groups with torsion, Canad. Math. Bul l., 57 (2014) 326-334.

[3] S. I. Adian, The Burnside problem and identities in groups, Ergebnisse der Mathematik und ihrer Grenzgebiete, 95, Springer-Verlag, Berlin-New York, 1979.