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### Seminar Geometrische Gruppentheorie: Agatha Atkarskaya (Hebrew University of Jerusalem) Vortrag: Combinatorial approach for Burnside groups of relatively small odd exponents

##### Thursday, 24.06.2021 15:00 per ZOOM: Link to Zoom info

Abstract: In order to have a better understanding of our mathematical world, it seems to be of a big interest to study algebraic systems with unusual and even counter-intuitive properties. We consider a free group in a variety of groups with the identity $w^n = 1$. Namely, we study the group $$B(m, n) = \langle x_1, \ldots, x_m \mid w^n = 1, w\in \langle x_1, \ldots, x_m\rangle \ldots \rangle,$$ it is called a free Burnside group of exponent~$n$. That is, the order of all elements in $B(n, m)$ is bounded by~$n$ which does not depend on a particular element. The question whether $B(n, m)$ is finite or infinite is in the spirit of such questions about objects with exotic properties and is called the general Burnside problem (stated by Burnside in 1902). The first solution of this problem was obtained in 1972 by Novikov and Adian for odd $n\geqslant 4381$, and then in 1982 by Olshanskii using different methods. We study $B(n, m)$ for $m \geqslant 2$ and odd numbers $n$ and our method gives a clear intuition why this group is infinite for big enough $n$. I will tell which effects make $B(n, m)$ to be infinite for odd $n \geqslant 297$. Joint work with Professor Eliyahu Rips and Professor Katrin Tent

Angelegt am Wednesday, 16.06.2021 13:26 von juschult
Geändert am Wednesday, 16.06.2021 13:26 von juschult
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