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 Mat. Zametki, 2008, Volume 83, Issue 3, Pages 323–332 (Mi mz4113)

Groups with Periodic Defining Relations

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: In the paper, the solvability of the word problem and the conjugacy problem is proved for a wide class of finitely presented groups defined by periodic defining relations of a sufficiently large odd degree. In the proof, we use a certain simplified version of the classification of periodic words and transformations of these words, which was presented in detail in the author's monograph devoted to the well-known Burnside problem. The result is completed with the proof of an interesting result of Sarkisyan on the existence of a group, given by defining relations of the form $E_i^2=1$, for which the word problem is unsolvable. This result was first published in abstracts of papers of the 13th All-Union Algebra Symposium in Gomel in 1975.

Keywords: finitely presented group, periodic defining relations, unsolvable conjugacy problem, unsolvable word problem, reduced word

DOI: https://doi.org/10.4213/mzm4113

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English version:
Mathematical Notes, 2008, 83:3, 293–300

Bibliographic databases:

UDC: 512.54

Citation: S. I. Adian, “Groups with Periodic Defining Relations”, Mat. Zametki, 83:3 (2008), 323–332; Math. Notes, 83:3 (2008), 293–300

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/mz4113
• https://doi.org/10.4213/mzm4113
• http://mi.mathnet.ru/eng/mz/v83/i3/p323

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. S. I. Adian, “The Burnside problem and related topics”, Russian Math. Surveys, 65:5 (2010), 805–855
2. S. I. Adian, “New estimates of odd exponents of infinite Burnside groups”, Proc. Steklov Inst. Math., 289 (2015), 33–71
3. Adian S.I. Atabekyan V.S., “N-Torsion Groups”, J. Contemp. Math. Anal.-Armen. Aca., 54:6 (2019), 319–327
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