Atabekyan, V. S.; Aslanyan, H. T.; Grigoryan, A. E. Normal automorphisms of free Burnside groups of period 3. (English) Zbl 1382.20043 Armen. J. Math. 9, No. 2, 60-67 (2017). Summary: If any normal subgroup of a group \(G\) is \(\phi\)-invariant for some automorphism \(\phi\) of \(G\), then \(\phi\) is called a normal automorphism. Each inner automorphism of a group is normal, but the converse is not true in the general case. We prove that any normal automorphism of the free Burnside group \(\mathbf{B}(m,3)\) of period 3 is inner for each rank \(m\geq3\). MSC: 20F50 Periodic groups; locally finite groups 20F28 Automorphism groups of groups 20E36 Automorphisms of infinite groups 20E05 Free nonabelian groups Keywords:normal automorphism; inner automorphism; periodic group; free Burnside group; free group PDFBibTeX XMLCite \textit{V. S. Atabekyan} et al., Armen. J. Math. 9, No. 2, 60--67 (2017; Zbl 1382.20043) Full Text: Link References: [1] A. Lubotzky, Normal automorphisms of free groups, J. Algebra, 63 (1980), no.2, pp. 494-498. · Zbl 0432.20025 [2] V. S. Atabekyan, Normal automorphisms of free Burnside groups, Izvestiya: Mathematics, 75(2011), no.2, pp. 223-237. · Zbl 1227.20030 [3] M. V. Neshadim, Free products of groups have no outer normal automorphisms, Algebra and Logic, 35(1996), no. 5, pp.316-318. [4] A. Minasyan, D. Osin, Normal automorphisms of relatively hyperbolic groups, Transaction of the Amer. Math. Soc., 362(2010), no. 11, pp. 6079-6103. · Zbl 1227.20041 [5] E. A. Cherepanov, Normal automorphisms of free Burnside groups of large odd exponents, Internat. J. Algebra Comput, 16 (2006), no. 5, pp. 839-847. · Zbl 1115.20024 [6] S. I. Adian, The Burnside problem and identities in groups, Ergeb. Math. Grenzgeb., 95, Springer-Verlag, Berlin,New York, 1979. P. 312. [7] S. I. Adian, New estimates of odd exponents of infinite Burnside groups, Proc. Steklov Inst. Math., 289 (2015), pp. 33-71. · Zbl 1343.20040 [8] V. S. Atabekyan, Automorphism groups and endomorphism semigroups of groups B(m,n), Algebra and Logic, 54(2015), no. 1, pp. 85-91. · Zbl 1323.20031 [9] V. S. Atabekyan, H. T. Aslanyan, H. A. Grigoryan, A. E. Grigoryan, Analogues of Nielsen’s and Magnus’s theorems for free Burnside groups of period 3, Proceedings of YSU, Physics and Mathematics, 51 (2017), no. 3, pp. 217-223. · Zbl 1386.20022 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.