Probabilistic identities in Burnside groups of exponent $3$

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 $m \ge 1$.