Product of two commutators as a square in a free group. (English) Zbl 0654.20030
It is shown that, if \([s,t][u,v]=x\) 2 in a free group, x need not be a commutator. The example is created by use of a result of D. Piollet which characterizes solutions of such equations using an algebraic interpretation of the mapping class group of the corresponding surface.
Reviewer: J.Comerford
MSC:
20F05 | Generators, relations, and presentations of groups |
20E05 | Free nonabelian groups |
20F12 | Commutator calculus |