Groups with Periodic Defining Relations
Matematičeskie zametki, Tome 83 (2008) no. 3, pp. 323-332
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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.
S. I. Adian. Groups with Periodic Defining Relations. Matematičeskie zametki, Tome 83 (2008) no. 3, pp. 323-332. http://geodesic.mathdoc.fr/item/MZM_2008_83_3_a0/
@article{MZM_2008_83_3_a0,
author = {S. I. Adian},
title = {Groups with {Periodic} {Defining} {Relations}},
journal = {Matemati\v{c}eskie zametki},
pages = {323--332},
year = {2008},
volume = {83},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_2008_83_3_a0/}
}
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[3] O. A. Sarkisyan, Problema ravenstva slov dlya nekotorykh klassov grupp i polugrupp, Dis. ...kand. fiz.-matem. nauk, MGU, M., 1983