Geodesic
Splitting automorphisms of free Burnside groups
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2011), pp. 62-64 Cet article a éte moissonné depuis la source Math-Net.Ru

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We have proved, that if $n\geq1003$ is an arbitrary odd number and $\varphi$ is a splitting automorphism of period $n$ of group $B(m, n)$ that has a prime order, then $\varphi$ is inner automorphism.
Keywords: splitting automorphism, free Burside group, holomorph of the group. 
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V. S. Atabekyan. Splitting automorphisms of free Burnside groups. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2011), pp. 62-64. http://geodesic.mathdoc.fr/item/UZERU_2011_3_a9/

[1] O.H. Kegel, “Die Nilpotenz der $H_p$-Gruppen”, Math. Z., 75 (1961), 373–376 | DOI | MR | Zbl

[2] J.G. Thompson, “Finite groups with fixed-point-free automorphisms of prime order”, Proc. Nat. Acad. Sci. USA, 45 (1959), 578–581 | DOI | MR | Zbl

[3] E.I. Khukhro, “Nilpotency of solvable groups that admit a splitting automorphism of prime order”, Algebra i Logika, 19:1 (1980), 118–129 | DOI | MR | Zbl

[4] S.I. Adian, The Burnside Problem and Identities in Groups, Ergeb. Math. Grenzgeb, 95, Springer-Verlag, Berlin-New York, 1979 | MR

[5] Russian Math. Surveys, 65:5 (2010), 805–855 | DOI | DOI | MR | Zbl

[6] V.D. Mazurov, Yu.I. Merzlyakov, V.A. Churkin (eds.), The Kourovka Notebook. Unsolved Problems in Group Theory, ed. 11, SB of RAS Institute of Math, Novosibirsk, 1990 | MR

[7] Math. USSR-Izv., 39:2 (1992), 905–957 | DOI | MR | Zbl

[8] Math. Notes, 82:4 (2007), 443–447 | DOI | DOI | MR | Zbl

[9] Izv. Math., 75:2 (2011), 223–237 | DOI | DOI | MR | Zbl