J. Aust. Math. Soc.
81 (2006), 199-208
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The palindromic width of a free product of groups
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Valery Bardakov
Institute of Mathematics
Siberian Branch Russian Academy of Science
630090 Novosibirsk
Russia
bardakov@math.nsc.ru
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Abstract
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Palindromes are those reduced words of free
products of groups that coincide with their
reverse words. We prove that a free product of
groups
has infinite palindromic width, provided that
is not the free product of two cyclic groups of
order two (Theorem 2.4). This means
that there is no uniform bound
such that every element of
is a product of at most
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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