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.
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
\Bibitem{Adi03}
\by S.~I.~Adian
\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
\publaddr Moscow
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\transl
\jour Proc. Steklov Inst. Math.
\yr 2011
\vol 272
\issue , suppl. 2
\pages S2--S12
\crossref{https://doi.org/10.1134/S0081543811030023}
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Linking options:
https://www.mathnet.ru/eng/spm2
https://doi.org/10.4213/spm2
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This publication is cited in the following 9 articles:
Ville Salo, Ilkka Törmä, “Independent finite automata on Cayley graphs”, Nat Comput, 16:3 (2017), 411
Ville Salo, Ilkka Törmä, Lecture Notes in Computer Science, 9099, Cellular Automata and Discrete Complex Systems, 2015, 224
V. S. Atabekyan, “Normal automorphisms of free Burnside groups”, Izv. Math., 75:2 (2011), 223–237
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., “Non-phi-admissible normal subgroups of free burnside groups”, Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences, 45:2 (2010), 112–122
V. S. Atabekyan, “Uniform Nonamenability of Subgroups of Free Burnside Groups of Odd Period”, Math. Notes, 85:4 (2009), 496–502
V. S. Atabekian, “On subgroups of free Burnside groups of odd exponent n⩾1003”, Izv. Math., 73:5 (2009), 861–892
V. S. Atabekyan, “The normalizers of free subgroups in free Burnside groups of odd period n⩾1003”, J. Math. Sci., 166:6 (2010), 691–703
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
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