J. Aust. Math. Soc.  81 (2006), 199-208
The palindromic width of a free product of groups

Valery Bardakov
  Institute of Mathematics
  Siberian Branch Russian Academy of Science
  630090 Novosibirsk
Vladimir Tolstykh
  Department of Mathematics
  Yeditepe University
  34755 Istanbul

Palindromes are those reduced words of free products of groups that coincide with their reverse words. We prove that a free product of groups $G$ has infinite palindromic width, provided that $G$ is not the free product of two cyclic groups of order two (Theorem 2.4). This means that there is no uniform bound $k$ such that every element of $G$ is a product of at most $k$ palindromes. Earlier, the similar fact was established for non-abelian free groups. The proof of Theorem 2.4 makes use of the ideas by Rhemtulla developed for the study of the widths of verbal subgroups of free products.
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