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Paper   IPM / M / 7703
School of Mathematics
  Title:   Writing certain commutators as products of cubes in free groups
  Author(s):  M. Akhavan-Malayeri
  Status:   Published
  Journal: J. Pure Appl. Algebra
  Vol.:  177
  Year:  2003
  Pages:   1-4
  Supported by:  IPM
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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