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 Sovrem. Probl. Mat., 2003, Issue 1, Pages 5–28 (Mi spm2)

The Burnside Problem on Periodic Groups, and Related Problems

Abstract: In a 1959–1975 cycle of papers, P.S. Novikov and S.I. Adian created a new method for studying periodic groups based on the classification of periodic words by means of a complicated simultaneous induction. The method was developed for solving the well-known Burnside problem on periodic groups, but it also enabled the authors to solve a number of other difficult problems of group theory. An extended survey of results contained in the cycle of papers mentioned above and of other significant results obtained after 1975 by Adian and other authors on the basis of the developed theory and its modifications is presented.

DOI: https://doi.org/10.4213/spm2

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2011, 272, suppl. 2, S2–S12

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Document Type: Article

Citation: S. I. Adian, “The Burnside Problem on Periodic Groups, and Related Problems”, Sovrem. Probl. Mat., 1, Steklov Math. Institute of RAS, Moscow, 2003, 5–28; Proc. Steklov Inst. Math., 272, suppl. 2 (2011), S2–S12

Citation in format AMSBIB
\paper The Burnside Problem on Periodic Groups, and Related Problems
\serial Sovrem. Probl. Mat.
\yr 2003
\vol 1
\pages 5--28
\publ Steklov Math. Institute of RAS
\mathnet{http://mi.mathnet.ru/spm2}
\crossref{https://doi.org/10.4213/spm2}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2141821}
\zmath{https://zbmath.org/?q=an:1291.20034}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2011
\vol 272
\issue , suppl. 2
\pages S2--S12
\crossref{https://doi.org/10.1134/S0081543811030023}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79954610211}

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This publication is cited in the following articles:
1. L. D. Beklemishev, I. G. Lysenok, A. A. Mal'tsev, S. P. Novikov, M. R. Pentus, A. A. Razborov, A. L. Semenov, V. A. Uspenskii, “Sergei Ivanovich Adian (on his 75th birthday)”, Russian Math. Surveys, 61:3 (2006), 575–588
2. V. S. Atabekyan, “Uniform Nonamenability of Subgroups of Free Burnside Groups of Odd Period”, Math. Notes, 85:4 (2009), 496–502
3. V. S. Atabekian, “On subgroups of free Burnside groups of odd exponent $n\ge 1003$”, Izv. Math., 73:5 (2009), 861–892
4. V. S. Atabekyan, “The normalizers of free subgroups in free Burnside groups of odd period $n\ge1003$”, J. Math. Sci., 166:6 (2010), 691–703
5. Atabekyan V.S., “Non-phi-admissible normal subgroups of free burnside groups”, Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences, 45:2 (2010), 112–122
6. V. S. Atabekyan, “Normal automorphisms of free Burnside groups”, Izv. Math., 75:2 (2011), 223–237
7. V. S. Atabekyan, “On normal subgroups in the periodic products of S. I. Adian”, Proc. Steklov Inst. Math., 274 (2011), 9–24
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