The groups of automorphisms are complete for free Burnside groups of odd exponents \(n\geq 1003\). (Q2854969)
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scientific article; zbMATH DE number 6219292
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The groups of automorphisms are complete for free Burnside groups of odd exponents \(n\geq 1003\). |
scientific article; zbMATH DE number 6219292 |
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24 October 2013
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automorphism towers
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complete groups
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free Burnside groups
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automorphism groups
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inner automorphisms
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0.8974929
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0.87665236
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0.8627001
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0.8619306
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0.8593737
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0.85721076
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The groups of automorphisms are complete for free Burnside groups of odd exponents \(n\geq 1003\). (English)
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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 \(\Aut(B(m,n))\) 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 \(\Aut(B(m,n))\).
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