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Izv. RAN. Ser. Mat., 2011, Volume 75, Issue 2, Pages 3–18 (Mi izv4256)  

This article is cited in 19 scientific papers (total in 19 papers)

Normal automorphisms of free Burnside groups

V. S. Atabekyan

Yerevan State University

Abstract: We prove that for an arbitrary odd $n\ge1003$ and $m>1$ every automorphism of the free Burnside group $B(m,n)$ that stabilizes every maximal normal subgroup $N\trianglelefteq B(m,n)$ of infinite index is an inner automorphism. For the same values of $m$ and $n$, we establish that the subgroup of inner automorphisms of $\operatorname{Aut}(B(m,n))$ is maximal among the subgroups in which the orders of the elements are bounded by $n$.

Keywords: free Burnside group, normal automorphism, inner automorphism, maximal subgroup, non-Abelian simple group.


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English version:
Izvestiya: Mathematics, 2011, 75:2, 223–237

Bibliographic databases:

UDC: 512.54+512.543+512.544.43
MSC: 20E36, 20F05, 20F50, 20E32
Received: 10.11.2009

Citation: V. S. Atabekyan, “Normal automorphisms of free Burnside groups”, Izv. RAN. Ser. Mat., 75:2 (2011), 3–18; Izv. Math., 75:2 (2011), 223–237

Citation in format AMSBIB
\by V.~S.~Atabekyan
\paper Normal automorphisms of free Burnside groups
\jour Izv. RAN. Ser. Mat.
\yr 2011
\vol 75
\issue 2
\pages 3--18
\jour Izv. Math.
\yr 2011
\vol 75
\issue 2
\pages 223--237

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    This publication is cited in the following articles:
    1. S. I. Adian, “The Burnside problem and related topics”, Russian Math. Surveys, 65:5 (2010), 805–855  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. V. S. Atabekyan, “On normal subgroups in the periodic products of S. I. Adian”, Proc. Steklov Inst. Math., 274 (2011), 9–24  mathnet  crossref  mathscinet  isi  elib  elib
    3. Atabekyan V.S., Gevorgyan A.L., “On outer normal automorphisms of periodic products of groups”, J. Contemp. Mathemat. Anal., 46:6 (2011), 289–292  crossref  mathscinet  zmath  isi  elib  scopus
    4. Pahlevanyan A.S., “The Fibonacci automorphism of free Burnside groups”, RAIRO Theor. Inform. Appl., 45:3 (2011), 301–309  crossref  mathscinet  isi  elib  scopus
    5. V. S. Atabekyan, “Splitting automorphisms of free Burnside groups”, Uch. zapiski EGU, ser. Fizika i Matematika, 2011, no. 3, 62–64  mathnet
    6. Bardakov V., Vesnin A., Yadav M.K., “Class preserving automorphisms of unitriangular groups”, Internat. J. Algebra Comput., 22:3 (2012), 1250023, 17 pp.  crossref  mathscinet  zmath  isi  elib  scopus
    7. A. L. Gevorgyan, “On automorphisms of periodic products of groups”, Uch. zapiski EGU, ser. Fizika i Matematika, 2012, no. 2, 3–9  mathnet
    8. V. S. Atabekyan, “Splitting automorphisms of free Burnside groups”, Sb. Math., 204:2 (2013), 182–189  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. Atabekyan V.S., “The groups of automorphisms are complete for free Burnside groups of odd exponents $n\ge 1003$”, Int. J. Algebr. Comput., 23:6 (2013), 1485–1496  crossref  mathscinet  zmath  isi  elib  scopus
    10. Kunyavskii B., “Local-global invariants of finite and infinite groups: around Burnside from another side”, Expo. Math., 31:3 (2013), 256–273  crossref  mathscinet  zmath  isi  elib  scopus
    11. V. S. Atabekyan, “The automorphism tower problem for free periodic groups”, Uch. zapiski EGU, ser. Fizika i Matematika, 2013, no. 2, 3–7  mathnet
    12. 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
    13. 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
    14. Atabekyan V.S., “the Automorphisms of Endomorphism Semigroups of Free Burnside Groups”, Int. J. Algebr. Comput., 25:4 (2015), 669–674  crossref  mathscinet  zmath  isi  elib  scopus
    15. M. V. Neschadim, “Vnutrennie avtomorfizmy i nekotorye ikh obobscheniya”, Sib. elektron. matem. izv., 13 (2016), 1383–1400  mathnet  crossref  mathscinet  zmath
    16. Atabekyan V.S., Aslanyan H.T., Grigoryan A.E., “Normal Automorphisms of Free Burnside Groups of Period 3”, Armen. J. Math., 9:2 (2017), 60–67  mathscinet  zmath  isi
    17. Adian S.I., Atabekyan V.S., “Periodic Products of Groups”, J. Contemp. Math. Anal.-Armen. Aca., 52:3 (2017), 111–117  crossref  mathscinet  zmath  isi  scopus
    18. V. S. Atabekyan, H. T. Aslanyan, “On fixed points of automorphisms”, Uch. zapiski EGU, ser. Fizika i Matematika, 53:3 (2019), 147–149  mathnet
    19. S. I. Adian, V. S. Atabekyan, “Normal Automorphisms of Free Groups of Infinitely Based Varieties”, Math. Notes, 108:2 (2020), 149–154  mathnet  crossref  crossref  mathscinet  isi  elib
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