The palindromic width of a free product of groups
- Autores: Valery Bardakov, Vladimir Tolstykh
- Localización: Journal of the Australian Mathematical Society, ISSN 1446-7887, Vol. 81, Nº 2, 2006, págs. 199-208
- Idioma: inglés
- DOI: 10.1017/s1446788700015822
- Enlaces
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Resumen
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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