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

This article is cited in 2 scientific papers (total in 2 papers)

Groups with Periodic Defining Relations

S. I. Adian

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

Full text: PDF file (431 kB)
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English version:
Mathematical Notes, 2008, 83:3, 293–300

Bibliographic databases:

Document Type: Article
UDC: 512.54
Received: 25.09.2007

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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  • 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
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    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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. S. I. Adian, “New estimates of odd exponents of infinite Burnside groups”, Proc. Steklov Inst. Math., 289 (2015), 33–71  mathnet  crossref  crossref  isi  elib
  • Математические заметки Mathematical Notes
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