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Normal automorphisms of free Burnside groups of period 3. (English) Zbl 1382.20043

Summary: If any normal subgroup of a group \(G\) is \(\phi\)-invariant for some automorphism \(\phi\) of \(G\), then \(\phi\) is called a normal automorphism. Each inner automorphism of a group is normal, but the converse is not true in the general case. We prove that any normal automorphism of the free Burnside group \(\mathbf{B}(m,3)\) of period 3 is inner for each rank \(m\geq3\).

MSC:

20F50 Periodic groups; locally finite groups
20F28 Automorphism groups of groups
20E36 Automorphisms of infinite groups
20E05 Free nonabelian groups
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References:

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