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The groups of automorphisms are complete for free Burnside groups of odd exponents \(n\geq 1003\). (English) Zbl 1283.20039
Let \(B(m,n)\) be the free Burnside group in \(m\) generators (\(m>1\)) of exponent \(n\). This paper is devoted to prove that, if \(n\) is odd and \(n\geq 1003\), then \(\operatorname{Aut}(B(m,n))\) is complete (i.e. it has trivial center and each of its automorphisms is inner). Moreover, the group of all inner automorphisms \(\mathrm{Inn}(B(m,n))\) is the unique normal subgroup in \(\operatorname{Aut}(B(m,n))\).

MSC:
20F50 Periodic groups; locally finite groups
20F28 Automorphism groups of groups
20E36 Automorphisms of infinite groups
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