Groups with periodic defining relations. (Q2517978)

Let \(G\) be a group defined by finitely many relations of the form \(A_i^{n_i}=1\), where all the exponents \(n_i\) are divisible by an odd number \(n\geq 665\) and let \(G\) have no involutions. Then the author shows in this paper that the word and conjugacy problems are solvable for the above \(G\). In the proof, a way similar to that defined in the author's book [The Burnside problem and identities in groups. (1979; Zbl 0417.20001)] is followed. A simplified version of the classification of periodic words (that was also described in that book) is used. As noted in the text, the existence of a group with unsolvable word problem (which is generated by involutions) is first given by Sarkisian in his thesis. Since this result was never published in any journal (honestly, if it was, I cannot reach it), I should accept the author of this paper is right and so assume that the proof of Sarkisian's result has some gaps. Thus, S. I. Adyan gives a valuable proof for Sarkisian's result.