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 Proceedings of the YSU, Physical and Mathematical Sciences, 2013, Issue 2, Pages 3–7 (Mi uzeru85)

Mathematics

The automorphism tower problem for free periodic groups

V. S. Atabekyan

Yerevan State University, Faculty of Mathematics and Mechanics

Abstract: We prove that the group of automorphisms $Aut(B(m;n))$ of the free Burnside group $B(m;n)$ is complete for every odd exponent $n\geq 1003$ and for any $m > 1$, that is it has a trivial center and any automorphism of $Aut(B(m;n))$ is inner. Thus, the automorphism tower problem for groups $B(m;n)$ is solved and it is showed that it is as short as the automorphism tower of the absolutely free groups. Moreover, we obtain that the group of all inner automorphisms $Inn(B(m;n))$ is the unique normal subgroup in $Aut(B(m;n))$ among all its subgroups, which are isomorphic to free Burnside group $B(s;n)$ of some rank $s$.

Keywords: automorphism tower, complete group, free Burnside group.

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MSC: Primary 20F50; 20F28; Secondary 20D45, 20E36, 20B27
Accepted:28.02.2013
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Citation: V. S. Atabekyan, “The automorphism tower problem for free periodic groups”, Proceedings of the YSU, Physical and Mathematical Sciences, 2013, no. 2, 3–7

Citation in format AMSBIB
\Bibitem{Ata13} \by V.~S.~Atabekyan \paper The automorphism tower problem for free periodic groups \jour Proceedings of the YSU, Physical and Mathematical Sciences \yr 2013 \issue 2 \pages 3--7 \mathnet{http://mi.mathnet.ru/uzeru85} 

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This publication is cited in the following articles:
1. A. E. Grigoryan, “Inner automorphisms of non-commutative analogues of the additive group of rational numbers”, Uch. zapiski EGU, ser. Fizika i Matematika, 2015, no. 1, 12–14
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