Groups with Periodic Defining Relations

S. I. Adian

Matematičeskie zametki, Tome 83 (2008) no. 3, pp. 323-332

Résumé

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.

Détail

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