“School of Mathematics”
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Paper IPM / M / 7703  


Abstract:  
Let CU(γ)be the minimal number of cubes required
to express an element γ of a free group F. We establish
a method for showing that certain equations do not have solutions
in free groups. Using it, we find CU(γ) for certain
elements of the derived subgroup of F. If W=FιC_{∞} is
the wreath product of F by the infinite cyclic group, we also
show that every element of W′ is a product of at most one
commutator and three cubes in W.
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