# The Burnside problem for relatively small odd exponents

Seminar

Speaker

Agatha Atkarskaya (Hebrew University of Jerusalem)

Date

30/11/2022 - 11:30 - 10:30Add to Calendar

`2022-11-30 10:30:00``2022-11-30 11:30:00``The Burnside problem for relatively small odd exponents``The Burnside problem asks if finitely generated groups with identity x^n = 1 are necessarily finite. In general, the answer is negative if the exponent n is large enough. The first negative solution for odd n at least 4381 was given by Novikov and Adian in 1968. Using different methods, this result was also proved by Olshanskii in 1982 for n > 10^10. The proof of Novikov and Adian is combinatorial, while the proof of Olshanskii is based on geometric considerations. We present a proof of the Burnside problem for odd exponents based on new combinatorial ideas, which is relatively short and works for relatively small odd exponents. Joint work with E. Rips and K. Tent.``Room 132 of math building``אוניברסיטת בר-אילן - Department of Mathematics``mathoffice@math.biu.ac.il``Asia/Jerusalem``public`Place

Room 132 of math building

Abstract

The Burnside problem asks if finitely generated groups with identity x^n = 1 are necessarily finite. In general, the answer is negative if the exponent n is large enough. The first negative solution for odd n at least 4381 was given by Novikov and Adian in 1968. Using different methods, this result was also proved by Olshanskii in 1982 for n > 10^10. The proof of Novikov and Adian is combinatorial, while the proof of Olshanskii is based on geometric considerations. We present a proof of the Burnside problem for odd exponents based on new combinatorial ideas, which is relatively short and works for relatively small odd exponents.

Joint work with E. Rips and K. Tent.

Last Updated Date : 28/11/2022