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

This article is cited in 1 scientific paper (total in 1 paper)

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.

Full text: PDF file (127 kB)
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Document Type: Article
MSC: Primary 20F50; 20F28; Secondary 20D45, 20E36, 20B27
Received: 09.02.2013
Accepted:28.02.2013
Language: English

Citation: V. S. Atabekyan, “The automorphism tower problem for free periodic groups”, Proceedings of the YSU, Physical and Mathematial Scineces, 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 Mathematial Scineces
\yr 2013
\issue 2
\pages 3--7
\mathnet{http://mi.mathnet.ru/uzeru85}


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    Citing articles on Google Scholar: Russian citations, English citations
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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  mathnet
  • Proceedings of the Yerevan State University, series Physical and Mathematical sciences
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