
Proceedings of the YSU, Physical and Mathematical Sciences, 2013, Issue 2, Pages 3–7
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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 Received: 09.02.2013 Accepted:28.02.2013
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V. S. Atabekyan, “The automorphism tower problem for free periodic groups”, Proceedings of the YSU, Physical and Mathematical Sciences, 2013, no. 2, 3–7
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\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 37
\mathnet{http://mi.mathnet.ru/uzeru85}
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This publication is cited in the following articles:

A. E. Grigoryan, “Inner automorphisms of noncommutative analogues of the additive group of rational numbers”, Uch. zapiski EGU, ser. Fizika i Matematika, 2015, no. 1, 12–14

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