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 by the proof of an interesting result of Sarkisyan on the existence of a group, given by defining relations of the form E 2 i = 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.
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References
S. I. Adyan [Adian], The Burnside Problem and Identities in Groups (Nauka, Moscow, 1975; Springer-Verlag, Berlin-Heidelberg-New York, 1979).
S. I. Adyan and V. G. Durnev, “Algorithmic problems for groups and semigroups,” Uspekhi Mat. Nauk 55(2), 3–94 (2000) [Russian Math. Surveys 55 (2), 207–296 (2000)].
O. A. Sarkisyan, Word Problem for Some Classes of Groups and Semigroups, Candidate’s Dissertation in Mathematics and Physics (MGU, Moscow, 1983) [in Russian].
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Original Russian Text © S. I. Adyan, 2008, published in Matematicheskie Zametki, 2008, Vol. 83, No. 3, pp. 323–332.
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Adyan, S.I. Groups with periodic defining relations. Math Notes 83, 293–300 (2008). https://doi.org/10.1134/S0001434608030012
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DOI: https://doi.org/10.1134/S0001434608030012