This article is cited in 1 paper

Mathematics

Powers of subsets in free periodic groups

V. S. Atabekyan^a, H. T. Aslanyan^b, S. T. Aslanyan<sup>c

a</sup> Yerevan State University
^b American University of Armenia, Yerevan
^c Russian-Armenian University, Yerevan

Abstract: It is proved that for every odd $n \ge 1039$ there are two words $u(x, y), v(x,y)$ of length $\le 2^{22}n^3$ over the group alphabet $\{x,y\}$ of the free Burnside group $B(2 ,n),$ which generate a free Burnside subgroup of the group $B(2,n)$. This implies that for any finite subset $S$ of the group $B(m,n)$ the inequality $|S^t|>4\cdot 2.9^{[\frac{t}{2^{22}s^3}]}$ holds, where $s$ is the smallest odd divisor of $n$ that satisfies the inequality $s \ge 1039$.

Keywords: power of subset, product of subset, Burnside group.

MSC: 20F50, 20F05

Received: 27.05.2022
Revised: 20.06.2022
Accepted: 27.06.2022

Language: English

DOI: 10.46991/PYSU:A/2022.56.2.043