The palindromic width of a free product of groups

الأصل · EN

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. This means that there is no a uniform bound k such that every element of G is a product of at most k palindromes. Earlier the similar fact established for non-abelian free groups.