PROBABILISTIC IDENTITIES IN BURNSIDE GROUPS OF EXPONENT 3

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Submitted: 2025-01-17; Published: 2025-01-17

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Abstract

Burnside groups B(m,n) are relatively free groups that are factor groups of the absolutely free group Fm 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 ≥ 1.