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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
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