Abstract
In this paper, we describe the automorphism groups of the endomorphism semigroups of free Burnside groups B(m, n) for odd exponents n ≥ 1003. We prove, that the groups Aut (B(m, n)) and Aut ( End (B(m, n))) are canonically isomorphic. In particular, if the groups Aut ( End (B(m, n))) and Aut ( End (B(k, n))) are isomorphic, then m = k.
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