Normal Automorphisms of Free Burnside Groups of Period 3

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Normal Automorphisms of Free Burnside Groups of Period 3 Varujan Atabekyan

If any normal subgroup of a group GG is ϕϕ-invariant for some automorphism ϕϕ of GG, then ϕϕ is called a normal automorphism. Each inner automorphism of a group is normal, but converse is not true in the general case. We prove that any normal automorphism of free Burnside group B(m,3)B(m,3) of period 3 is inner for all rank m≥3m≥3.

DOI: https://armjmath.sci.am/index.php/ajm/article/view/157 Armenian Journal of Mathematics, 9(2) 60-67

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Keywords

normal automorphism, inner automorphism, periodic group, free Burnside group, free group

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