Abstract:
We prove that for an arbitrary odd n⩾1003 and m>1 every automorphism of the free Burnside group B(m,n) that stabilizes every maximal normal subgroup 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.
\Bibitem{Ata11}
\by V.~S.~Atabekyan
\paper Normal automorphisms of free Burnside groups
\jour Izv. Math.
\yr 2011
\vol 75
\issue 2
\pages 223--237
\mathnet{http://mi.mathnet.ru/eng/im4256}
\crossref{https://doi.org/10.1070/IM2011v075n02ABEH002532}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2830240}
\zmath{https://zbmath.org/?q=an:1227.20030}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2011IzMat..75..223A}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000289889000001}
\elib{https://elibrary.ru/item.asp?id=20358782}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-80053544146}
Linking options:
https://www.mathnet.ru/eng/im4256
https://doi.org/10.1070/IM2011v075n02ABEH002532
https://www.mathnet.ru/eng/im/v75/i2/p3
This publication is cited in the following 21 articles:
Atabekyan V.S. Gevorkyan G.G., “Central Extensions of N-Torsion Groups”, J. Contemp. Math. Anal.-Armen. Aca., 57:1 (2022), 26–34
S. I. Adian, V. S. Atabekyan, “Normal Automorphisms of Free Groups of Infinitely Based Varieties”, Math. Notes, 108:2 (2020), 149–154
V. S. Atabekyan, H. T. Aslanyan, “On fixed points of automorphisms”, Uch. zapiski EGU, ser. Fizika i Matematika, 53:3 (2019), 147–149
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
Adian S.I., Atabekyan V.S., “Periodic Products of Groups”, J. Contemp. Math. Anal.-Armen. Aca., 52:3 (2017), 111–117
M. V. Neschadim, “Vnutrennie avtomorfizmy i nekotorye ikh obobscheniya”, Sib. elektron. matem. izv., 13 (2016), 1383–1400
V. S. Atabekyan, “Automorphism groups and endomorphism semigroups of groups B(m,n)”, Algebra and Logic, 54:1 (2015), 58–62
Atabekyan V.S., “the Automorphisms of Endomorphism Semigroups of Free Burnside Groups”, Int. J. Algebr. Comput., 25:4 (2015), 669–674
V. S. Atabekyan, “Splitting Automorphisms of Order p^k of Free Burnside Groups are Inner”, Math. Notes, 95:5 (2014), 586–589
V. S. Atabekyan, “Splitting automorphisms of free Burnside groups”, Sb. Math., 204:2 (2013), 182–189
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
Kunyavskii B., “Local-global invariants of finite and infinite groups: around Burnside from another side”, Expo. Math., 31:3 (2013), 256–273
V. S. Atabekyan, “The automorphism tower problem for free periodic groups”, Uch. zapiski EGU, ser. Fizika i Matematika, 2013, no. 2, 3–7
Bardakov V., Vesnin A., Yadav M.K., “Class preserving automorphisms of unitriangular groups”, Internat. J. Algebra Comput., 22:3 (2012), 1250023, 17 pp.
A. L. Gevorgyan, “On automorphisms of periodic products of groups”, Uch. zapiski EGU, ser. Fizika i Matematika, 2012, no. 2, 3–9
V. S. Atabekyan, “On normal subgroups in the periodic products of S. I. Adian”, Proc. Steklov Inst. Math., 274 (2011), 9–24
Atabekyan V.S., Gevorgyan A.L., “On outer normal automorphisms of periodic products of groups”, J. Contemp. Mathemat. Anal., 46:6 (2011), 289–292
Pahlevanyan A.S., “The Fibonacci automorphism of free Burnside groups”, RAIRO Theor. Inform. Appl., 45:3 (2011), 301–309
V. S. Atabekyan, “Splitting automorphisms of free Burnside groups”, Uch. zapiski EGU, ser. Fizika i Matematika, 2011, no. 3, 62–64
A. S. Pahlevanyan, H. R. Rostami, “On automorphisms and embeddings of free periodic groups”, J. Contemp. Mathemat. Anal., 46:2 (2011), 106
Citation in format AMSBIB
Contact us: