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Matematicheskie Zametki, 2008, Volume 83, Issue 3, Pages 323–332
DOI: https://doi.org/10.4213/mzm4113
(Mi mzm4113)
 

This article is cited in 8 scientific papers (total in 8 papers)

Groups with Periodic Defining Relations

S. I. Adian

Steklov Mathematical Institute, Russian Academy of Sciences
Full-text PDF (431 kB) Citations (8)
References:
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.
Received: 25.09.2007
English version:
Mathematical Notes, 2008, Volume 83, Issue 3, Pages 293–300
DOI: https://doi.org/10.1134/S0001434608030012
Bibliographic databases:
Document Type: Article
UDC: 512.54
Language: Russian
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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  • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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