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Mat. Sb., 2013, Volume 204, Number 2, Pages 31–38 (Mi msb7905)  

This article is cited in 7 scientific papers (total in 7 papers)

Splitting automorphisms of free Burnside groups

V. S. Atabekyan

Erevan State University, Armenia

Abstract: It is proved that, if the order of a splitting automorphism of odd period $n\ge1003$ of a free Burnside group $B(m,n)$ is a prime, then the automorphism is inner. This implies, for every prime $n\ge1009$, an affirmative answer to the question on the coincidence of the splitting automorphisms of period $n$ of the group $B(m,n)$ with the inner automorphisms (this question was posed in the “Kourovka Notebook” in 1990).
Bibliography: 17 titles.

Keywords: splitting automorphism, free Burnside group, inner automorphism, Tarski-monster, subdirect product.

Funding Agency Grant Number
State Committee on Science of the Ministry of Education and Science of the Republic of Armenia


DOI: https://doi.org/10.4213/sm7905

Full text: PDF file (470 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2013, 204:2, 182–189

Bibliographic databases:

UDC: 512.54+512.543+512.544.43
MSC: Primary 20F50; Secondary 20B27
Received: 30.06.2011 and 10.07.2012

Citation: V. S. Atabekyan, “Splitting automorphisms of free Burnside groups”, Mat. Sb., 204:2 (2013), 31–38; Sb. Math., 204:2 (2013), 182–189

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/msb/v204/i2/p31

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Atabekyan V.S., “The groups of automorphisms are complete for free Burnside groups of odd exponents $n\ge1003$”, Internat. J. Algebra Comput., 23:6 (2013), 1485–1496  crossref  mathscinet  zmath  isi  elib  scopus
    2. V. S. Atabekyan, “The automorphism tower problem for free periodic groups”, Uch. zapiski EGU, ser. Fizika i Matematika, 2013, no. 2, 3–7  mathnet
    3. V. S. Atabekyan, “Splitting Automorphisms of Order $p^k$ of Free Burnside Groups are Inner”, Math. Notes, 95:5 (2014), 586–589  mathnet  crossref  crossref  mathscinet  isi  elib
    4. V. S. Atabekyan, “Automorphism groups and endomorphism semigroups of groups $B(m,n)$”, Algebra and Logic, 54:1 (2015), 58–62  mathnet  crossref  crossref  mathscinet  isi
    5. A. L. Gevorgyan, Sh. A. Stepanyan, “On automorphisms of some periodic products of groups”, Uch. zapiski EGU, ser. Fizika i Matematika, 2015, no. 2, 7–10  mathnet
    6. V. S. Atabekyan, “The automorphisms of endomorphism semigroups of free Burnside groups”, Internat. J. Algebra Comput., 25:4 (2015), 669-674  crossref  mathscinet  zmath  isi  elib  scopus
    7. J. Contemp. Math. Anal., Armen. Acad. Sci., 52:3 (2017), 111–117  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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