Geodesic
Powers of subsets in free periodic groups
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 56 (2022) no. 2, pp. 43-48.

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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. 
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V. S. Atabekyan; H. T. Aslanyan; S. T. Aslanyan. Powers of  subsets in  free periodic groups. Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 56 (2022) no. 2, pp. 43-48. http://geodesic.mathdoc.fr/item/UZERU_2022_56_2_a0/

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