Geodesic
Probabilistic identities in Burnside groups of exponent $3$
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 58 (2024) no. 2, pp. 37-46

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Burnside groups $B(m, n)$ are relatively free groups that are factor groups of the absolutely free group $F_m$ of rank $m$ by its subgroup, generated by $n$-th degrees of all the elements. They are the largest groups of fixed rank that have the exponent equal to $n$. In this work we compute the commuting probability for free Burnside groups $B(m, 3)$ of exponent 3 and rank $m \ge 1$.
Keywords: probabilistic identities, Burnside groups, relatively free groups 
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     title = {Probabilistic  identities  in  {Burnside}  groups of exponent $3$},
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A. R. Fahradyan. Probabilistic  identities  in  Burnside  groups of exponent $3$. Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 58 (2024) no. 2, pp. 37-46. http://geodesic.mathdoc.fr/item/UZERU_2024_58_2_a0/