On the word problem in periodic group varieties. (English) Zbl 0727.20026
It is proved that for every odd \(n\geq 665\) and every \(p>1\) coprime to n the group variety with defining identities \(x^{np}=1\), \([x^ n,y^ n]=1\) has unsolvable word problem. It is the first known example of a periodic variety of groups with this property. The proof is hard, depending on the well known results of Novikov and Adyan.
Reviewer: L.A.Bokut’ (Novosibirsk)
MSC:
20F10 | Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) |
20F05 | Generators, relations, and presentations of groups |
20E10 | Quasivarieties and varieties of groups |
20F50 | Periodic groups; locally finite groups |