Abstract:
It is proved that, if the order of a splitting automorphism of odd period n⩾1003 of a free Burnside group B(m,n) is a prime, then the automorphism is inner. This implies, for every prime n⩾1009, 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.
\Bibitem{Ata13}
\by V.~S.~Atabekyan
\paper Splitting automorphisms of free Burnside groups
\jour Sb. Math.
\yr 2013
\vol 204
\issue 2
\pages 182--189
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This publication is cited in the following 9 articles:
Gevorgyan A.L. Gevorgyan G.G., “Finite Subgroups of the Relatively Free N-Torsion Groups”, J. Contemp. Math. Anal.-Armen. Aca., 55:1 (2020), 1–4
V. S. Atabekyan, H. T. Aslanyan, “On fixed points of automorphisms”, Uch. zapiski EGU, ser. Fizika i Matematika, 53:3 (2019), 147–149
J. Contemp. Math. Anal., Armen. Acad. Sci., 52:3 (2017), 111–117
V. S. Atabekyan, “Automorphism groups and endomorphism semigroups of groups B(m,n)”, Algebra and Logic, 54:1 (2015), 58–62
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
V. S. Atabekyan, “The automorphisms of endomorphism semigroups of free Burnside groups”, Internat. J. Algebra Comput., 25:4 (2015), 669-674
V. S. Atabekyan, “Splitting Automorphisms of Order pk of Free Burnside Groups are Inner”, Math. Notes, 95:5 (2014), 586–589
Atabekyan V.S., “The groups of automorphisms are complete for free Burnside groups of odd exponents n⩾1003”, Internat. J. Algebra Comput., 23:6 (2013), 1485–1496
V. S. Atabekyan, “The automorphism tower problem for free periodic groups”, Uch. zapiski EGU, ser. Fizika i Matematika, 2013, no. 2, 3–7
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